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Physical Chemistry : Quantum Mechanics - Horia Metiu

Physical Chemistry

Quantum Mechanics


Published: 21st February 2006
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This is a new undergraduate textbook on physical chemistry by Horia Metiu published as four separate paperback volumes. These four volumes on physical chemistry combine a clear and thorough presentation of the theoretical and mathematical aspects of the subject with examples and applications drawn from current industrial and academic research. By using the computer to solve problems that include actual experimental data, the author is able to cover the subject matter at a practical level. The books closely integrate the theoretical chemistry being taught with industrial and laboratory practice. This approach enables the student to compare theoretical projections with experimental results, thereby providing a realistic grounding for future practicing chemists and engineers. Each volume of Physical Chemistry includes Mathematica(R) and Mathcad(R) Workbooks on CD-ROM.
Metiu's four separate volumes-Thermodynamics, Statistical Mechanics, Kinetics, and Quantum Mechanics-offer built-in flexibility by allowing the subject to be covered in any order.
These textbooks can be used to teach physical chemistry without a computer, but the experience is enriched substantially for those students who do learn how to read and write Mathematica(R) or Mathcad(R) programs. A TI-89 scientific calculator can be used to solve most of the exercises and problems.

(R) Mathematica is a registered trademark of Wolfram Research, Inc.
(R) Mathcad is a registered trademark of Mathsoft Engineering & Education, Inc.

Horia Metiu has created a significant set of volumes on undergraduate physical chemistry. The integration of Mathematica and Mathcad workbooks into the four texts provides instructors with an attractive new option in teaching. Metiua's writing style is folksy and the graphics minimal, a refreshing approach|.Taken as a whole, the four volumes on physical chemistry by Metiu are impressive, particularly Thermodynamics and Quantum Mechanics|.Without a doubt, the four textbooks provide essential materials of great utility to physical chemistry instructors. The bottom line is that the set of four volumes is a must have-a keeper- as a novel resource or invaluable classroom tool.

Journal of Chemical Education

February 2008, Vol. 85, No. 2, p. 206

Prefacep. xxi
How to use the workbooks, exercises, and problemsp. xxvii
Why quantum mechanics?p. 1
Molecular vibrationsp. 1
Radiation by a hot bodyp. 2
The stability of atomsp. 3
Dynamic variables and operatorsp. 5
Operators: the definitionp. 5
Examples of operatorsp. 6
Operations with operatorsp. 7
Operator additionp. 7
Operator multiplicationp. 8
Powers of operatorsp. 9
The commutator of two operatorsp. 9
Linear operatorsp. 11
Dynamical variables as operatorsp. 11
Position and potential energy operatorsp. 12
Potential energy operatorp. 13
The momentum operatorp. 14
The kinetic energy operatorp. 14
The total energy (the Hamiltonian)p. 16
Angular momentump. 17
Review of complex numbersp. 21
Complex functions of real variablesp. 24
The eigenvalue problemp. 25
The eigenvalue problem: definition and examplesp. 25
The eigenvalue problem for p[subscript x]p. 26
p[subscript x] has an infinite number of eigenvaluesp. 26
The eigenvalue problem for angular momentump. 27
If two operators commute, they have the same eigenfunctionsp. 29
Degenerate eigenvaluesp. 30
Which eigenfunctions have a meaning in physics?p. 32
Not all eigenfunctions are physically meaningfulp. 32
Normalizationp. 32
A relaxed conditionp. 33
An example: the eigenfunctions of kinetic energyp. 34
One-dimensional motion in the force-free, unbounded spacep. 34
The eigenfunctions of the kinetic energy operatorp. 35
Which of these eigenfunctions can be normalized?p. 37
Boundary conditions: the particle in a boxp. 38
Forcing the eigenfunctions to satisfy the boundary conditionsp. 38
Quantizationp. 40
The particle cannot have zero kinetic energyp. 40
Imposing the boundary conditions removes the trouble with normalizationp. 42
Some properties of eigenvalues and eigenfunctionsp. 42
What do we measure when we study quantum systems?p. 45
Introductionp. 45
The preparation of the initial statep. 46
Not all quantum systems have "well-defined" energyp. 46
Three examples of energy eigenstatesp. 48
A particle in a one-dimensional boxp. 49
The vibrational energy of a diatomic moleculep. 50
The energy eigenstates of the hydrogen atomp. 51
Energy measurements by electron scatteringp. 52
Electron scattering from a gas of diatomic moleculesp. 53
Energy measurements by photon emissionp. 57
Photon emissionp. 57
Applicationsp. 58
Some results are certain, most are just probablep. 61
Introductionp. 61
What is the outcome of an electron-scattering experiment?p. 62
Classical interpretation of the experimentp. 63
The quantum description of the experimentp. 64
Probabilitiesp. 65
A discussion of photon absorption measurementsp. 68
Why the outcome of most absorption experiments is certainp. 69
A discussion of photon emission measurementsp. 69
A one-photon, one-molecule experimentp. 70
The probabilities of different eventsp. 72
The physical interpretation of the wave functionp. 73
Application to a vibrating diatomic moleculep. 75
Data for HClp. 76
Interpretationp. 79
Average valuesp. 79
The effect of position uncertainty on a diffraction experimentp. 80
The effect of position uncertainty in an ESDAID experimentp. 81
Tunnelingp. 85
Classically forbidden regionp. 85
How large is the accessible region?p. 85
The classically allowed region for an oscillatorp. 86
Tunneling depends on mass and energyp. 89
Tunneling junctionsp. 90
Scanning tunneling microscopyp. 91
Particle in a boxp. 95
Define the systemp. 95
The classical Hamiltonianp. 96
Quantizing the systemp. 97
The boundary conditionsp. 98
Solving the eigenvalue problem (the Schrodinger equation) for the particle in a boxp. 100
Separation of variablesp. 100
Boundary conditionsp. 101
The behavior of a particle in a boxp. 104
The ground state energy is not zerop. 105
Degeneracyp. 107
Degeneracy is related to the symmetry of the systemp. 109
The eigenfunctions are normalizedp. 111
Orthogonalityp. 112
The position of a particle in a given statep. 113
Light emission and absorption: the phenomenap. 117
Introductionp. 117
Light absorption and emission: the phenomenap. 118
An absorption experimentp. 118
Characterization of an absorption spectrump. 119
Why the transmitted intensity is low at certain frequenciesp. 120
Emission spectroscopyp. 122
Unitsp. 126
How to convert from one unit to anotherp. 128
Why we need to know the laws of light absorption and emissionp. 130
Light emission and absorption: Einstein's phenomenological theoryp. 135
Introductionp. 135
Photon absorption and emission: the modelp. 136
Photon energy and energy conservationp. 136
How to reconcile this energy conservation with the existence of a line-widthp. 137
The modelp. 137
Photon absorption and emission: the rate equationsp. 138
The rate of photon absorptionp. 138
The rate of spontaneous photon emissionp. 139
The rate of stimulated emissionp. 140
The total rate of change of N[subscript 0] (or N[subscript 1])p. 140
Photon absorption and emission: the detailed balancep. 141
Molecules in thermal equilibrium with radiationp. 141
The detailed balancep. 143
The solution of the rate equationsp. 144
Using the detailed balance results to simplify the rate equationp. 145
The initial conditionsp. 146
The ground state population when the molecules are continuously exposed to lightp. 146
Analysis of the result: saturationp. 147
Why Einstein introduced stimulated emissionp. 149
Simulated emission and the laserp. 150
The rate of population relaxationp. 151
Light absorption: the quantum theoryp. 153
Introductionp. 153
Quantum theory of light emission and absorptionp. 154
The absorption probabilityp. 154
Electrodynamic quantities: light pulsesp. 154
Electromagnetic quantities: the polarization of lightp. 156
Electromagnetic properties: the direction of propagationp. 157
Electromagnetic quantities: the energy and the intensity of the pulsep. 157
The properties of the molecule: the transition dipole moment <[psi subscript f vertical bar]m[vertical bar psi subscript i]>p. 158
The properties of the molecule: the line shapep. 159
How the transition probability formula is usedp. 162
The probability of stimulated emissionp. 163
Validity conditionsp. 163
The connection to Einstein's B coefficientp. 163
Single molecule spectroscopy and the spectroscopy of an ensemble of moleculesp. 165
Light emission and absorption by a particle in a box and a harmonic oscillatorp. 169
Introductionp. 169
Light absorption by a particle in a boxp. 170
Quantum dotsp. 170
Photon absorption probabilityp. 172
The amount of light and its frequencyp. 173
The energies and absorption frequenciesp. 173
The transition dipolep. 174
The energy eigenfunctions for a particle in a boxp. 174
The dipole operator mp. 175
The role of light polarizationp. 176
The evaluation of the transition moment for a particle in a boxp. 176
The first selection rulep. 178
Physical interpretationp. 178
The second selection rulep. 178
A calculation of the spectrum in arbitrary unitsp. 180
Light absorption by a harmonic oscillatorp. 181
The eigenstates and eigenvalues of a harmonic oscillatorp. 183
The transition dipolep. 183
The molecular orientation and polarizationp. 184
Two-particle systemsp. 187
Introductionp. 187
The Schrodinger equation for the internal motionp. 189
The laboratory coordinate systemp. 189
The energyp. 190
Because there is no external force, the system moves with constant velocityp. 191
A coordinate system with the origin in the center of massp. 194
The total energy in terms of momentump. 195
The Hamiltonian operatorp. 196
The concept of quasi-particlep. 197
The Hamiltonian of the quasi-particle in spherical coordinatesp. 199
The role of angular momentum in the motion of the two-particle systemp. 201
Angular momentum in classical mechanicsp. 201
The properties of angular momentump. 201
The Schrodinger equation of the quasi-particle and the square of the angular momentump. 205
The role of angular momentum in the motion of the two-particle systemp. 207
The evolution of the angular momentump. 207
A polar coordinate systemp. 208
The angular momentum in polar coordinatesp. 210
The energy in polar coordinatesp. 210
Angular momentum in quantum mechanicsp. 213
Introductionp. 213
The operators representing the angular momentum in quantum mechanicsp. 215
Angular momentum in classical mechanicsp. 215
The angular momentum operator in quantum mechanicsp. 216
Angular momentum in spherical coordinatesp. 217
The operator L[superscript 2]p. 218
The commutation relations between L[superscript 2] and L[subscript x], L[subscript y], L[subscript z]p. 218
The eigenvalue equations for L[superscript 2] and L[subscript z]p. 220
The eigenvalue problem for L[superscript 2]p. 221
The eigenvalue problem for L[subscript z]p. 222
Spherical harmonicsp. 222
The physical interpretation of these eigenstatesp. 225
A brief explanation of the procedure for changing coordinatesp. 226
Two particle systems: the radial and angular Schrodinger equationsp. 231
Introductionp. 231
The Schrodinger equation in terms of L[superscript 2]p. 232
The Hamiltonian of a two-particle system in terms of L[superscript 2]p. 232
The radial and the angular Schrodinger equationsp. 233
The separation of variables in the Schrodinger equationp. 233
Additional physical conditionsp. 234
The integral over the anglesp. 235
The radial normalizationp. 235
The energy eigenstates of a diatomic moleculep. 239
Introductionp. 239
The harmonic approximationp. 240
The form of the function V(r)p. 240
The physics described by V(r)p. 241
When the approximation is correctp. 244
The harmonic approximation to V(r)p. 245
The rigid-rotor approximationp. 247
Physical interpretationp. 247
The rigid-rotor approximation decouples vibrational and rotational motionp. 248
The eigenstates and eigenvalues of the radial Schrodinger equation in the harmonic and rigid-rotor approximationp. 249
The eigenvaluesp. 249
An improved formula for the energyp. 250
The radial eigenfunctionsp. 252
The physical interpretation of the eigenfunctionsp. 254
The probability of having a given interatomic distance and orientationp. 255
The probability of having a given bond lengthp. 256
Turning point and tunnelingp. 258
The average values of r - r[subscript 0] and (r - r[subscript 0])[superscript 2]p. 260
The energy eigenstates and eigenvalues of a diatomic moleculep. 262
Diatomic molecule: its spectroscopyp. 265
Introductionp. 265
Collect the necessary equationsp. 269
The frequencies of the absorbed photonsp. 269
Photon absorption and emission probabilitiesp. 271
The wave function for the nuclear motionp. 272
The electronic wave functionp. 273
The dipole moment of the moleculep. 274
The separation of the transition dipole matrix element into a rotational and vibrational contributionp. 275
The harmonic approximation for the dipole momentp. 277
Physical interpretationp. 279
The integral <l[subscript f], m[subscript f vertical bar]cos([theta])[vertical bar]l[subscript i], m[subscript i]>p. 280
Vibrational and rotational excitation by absorption of an infrared photonp. 281
The molecules in a gas have a variety of statesp. 285
The infrared absorption spectrum of a gas at a fixed temperaturep. 286
The probability of [characters not reproducible] (v, l, m; T)p. 288
The probability of various states in a gas: a numerical studyp. 289
Back to the spectrum: the relative intensity of the absorption peaksp. 291
Numerical analysisp. 291
The hydrogen atomp. 295
Introductionp. 295
The Schrodinger equation for a one-electron atomp. 296
Why the properties of a one-electron atom are so different from those of a diatomic moleculep. 297
The solution of the Schrodinger equation for a one-electron atomp. 299
The eigenvaluesp. 300
The eigenfunctionsp. 301
The energyp. 302
The magnitude of the energiesp. 302
The energy scale [epsilon] and the length scale ap. 304
The radial wave functions R[subscript n,l] (r) and the mean values of various physical quantitiesp. 306
The probability of finding the electron at a certain distance from the nucleusp. 308
The functions R[subscript n,l] (r)p. 310
Plots of R[subscript n,l] (r)p. 311
The mean values of r, r[superscript 2], Coulomb energy, centrifugal energy, and radial kinetic energyp. 312
The angular dependence of the wave functionp. 317
Some nomenclaturep. 319
The s-statesp. 319
The np orbitalsp. 320
The nd orbitalsp. 323
Hydrogen atom: absorption and emission spectroscopyp. 325
The transition dipolep. 327
The selection rulesp. 328
The radial integralsp. 330
The spin of the electron and its role in spectroscopyp. 331
Introductionp. 331
The spin operatorsp. 334
Spin eigenstates and eigenvaluesp. 335
The scalar productp. 337
The emission spectrum of a hydrogen atom in a magnetic field: the normal Zeeman effectp. 339
The experimentp. 340
A modern (but oversimplified) version of the Lorentz modelp. 342
The energy of the hydrogen atom in a magnetic fieldp. 343
The emission frequenciesp. 345
The spectrump. 347
The role of spin in light emission by a hydrogen atom: the anomalous Zeeman effectp. 348
The interaction between spin and a magnetic fieldp. 348
The energies of the electron in the hydrogen atom: the contribution of spinp. 348
Comments and warningsp. 350
The electronic structure of molecules: The H[subscript 2] moleculep. 353
Introductionp. 353
The Born-Oppenheimer approximationp. 355
The electronic energies E[subscript n] (R) are the potential energies for the nuclear motionp. 358
How to use the variational principlep. 363
Application to the harmonic oscillatorp. 363
An application of the variational principle that uses a basis setp. 366
The many-body wave function as a product of orbitalsp. 369
The curse of multi-dimensionalityp. 369
The wave function as a product of orbitalsp. 370
How to choose good orbitalsp. 372
The electron wave function must be antisymmetricp. 372
Indistinguishable particlesp. 372
The antisymmetrization of a product of orbitalsp. 375
How to generalize to more than two electronsp. 377
The Pauli principlep. 379
Which electrons should be antisymmetrizedp. 380
The molecular orbitals in a minimal basis set: [sigma subscript u] and [sigma subscript g]p. 383
The MO-LCAO methodp. 383
The minimal basis setp. 384
Determine the molecular orbitals by using symmetryp. 384
The molecular orbitals are normalizedp. 385
The symmetry of [sigma subscript g] and [sigma subscript u]p. 387
The antisymmetrized products used in the configuration interaction wave functions must be eigenfunctions of S[superscript 2] and S[subscript z]p. 387
The strategy for constructing the functions [Phi subscript i](1, 2)p. 389
The spin statesp. 389
The singlet state [vertical bar] 0, 0>p. 390
The triplet states [vertical bar] 1, m[subscript s]>p. 391
Pairing up the spin and the orbital functions to create antisymmetric configurationsp. 391
The states [Phi subscript 1], [Phi subscript 2], and [Phi subscript 6]p. 391
The states [Phi subscript 3], [Phi subscript 4], and [Phi subscript 5]p. 392
The notations [superscript 1 Sigma subscript g+], [superscript 1 Sigma subscript g-], [superscript 3 Sigma subscript u,-1], [superscript 3 Sigma subscript u,0], [superscript 3 Sigma subscript u,1], [superscript 1 Sigma subscript u,0]p. 392
The configurations in terms of atomic orbitals: physical interpretationp. 393
The integrals required by the configuration interaction methodp. 394
The overlap matrix is diagonalp. 395
Only the off-diagonal matrix elements <[Phi subscript 1 vertical bar]H[vertical bar Phi subscript 2]> and <[Phi subscript 2 vertical bar]H[vertical bar Phi subscript 1]> differ from zerop. 395
The Hamiltonian matrixp. 396
The Hamiltonian in atomic unitsp. 396
Atomic unitsp. 397
The matrix elements in terms of atomic orbitalsp. 397
Expression for the matrix elementsp. 398
The overlap integral S(R)p. 399
The integral J(R)p. 399
The integral K(R)p. 401
The integral J'(R)p. 401
The integral K'(R)p. 402
The integral L(R)p. 404
The ground and excited state energies given by perturbation theoryp. 405
Behavior of H[subscript 11] (R) at large Rp. 407
The configuration interaction methodp. 409
The variational eigenvalue problem: a summaryp. 409
The eigenvalues and the eigen vectors of matrix Hp. 410
The coupling between configurationsp. 411
When perturbation theory is accuratep. 412
The configuration interaction energiesp. 412
The configuration interaction wave function of the ground statep. 414
Summaryp. 416
Nuclear magnetic resonance and electron spin resonancep. 421
Introductionp. 421
More information about spin operators and spin statesp. 424
The NMR spectrum of a system with one independent spinp. 428
The energy of the spin states for non-interacting spinsp. 428
The energy levelsp. 429
The rate of energy absorptionp. 430
NMR notation and unitsp. 430
The order of magnitude of various quantitiesp. 431
Hot bandsp. 432
The chemical shiftp. 434
The magnetic field acting on a nucleus depends on environmentp. 434
The NMR spectrum of a system of two non-interacting nuclei having spin 1/2p. 436
The Hamiltonian and the states of a system of two non-interacting spin 1/2 particlesp. 436
The order of magnitude of these energiesp. 438
The selection rulesp. 438
The frequencies of the allowed transitionsp. 440
The spin-spin interactionp. 441
Spin-spin couplingp. 441
The interaction between nuclear spinsp. 442
The spectrum of two distinguishable, interacting nucleip. 443
The energies of the spin statesp. 443
The Hamiltonianp. 444
The states of the interacting spinsp. 444
The Galerkin method: how to turn an operator equation into a matrix equationp. 446
The matrix elements H[subscript nm] = <[psi subscript n vertical bar]H[vertical bar psi subscript m]>p. 447
Perturbation theoryp. 449
The off-diagonal elementsp. 450
The lowest energy E[subscript 1] and eigenvector [vertical bar phi subscript 1]>p. 451
The eigenvalue E[subscript 2] and the spin state [vertical bar phi subscript 2]>p. 452
Why [vertical bar phi subscript 1]> and [vertical bar phi subscript 2]> are so differentp. 453
The physical meaning of [vertical bar phi subscript 2]>p. 453
The states [vertical bar phi subscript 3]> and [vertical bar phi subscript 4]> and the energies E[subscript 3] and E[subscript 4]p. 455
The orders of magnitudep. 456
The NMR spectrum of two weakly interacting, indistinguishable nuclei having spin 1/2p. 457
The states that satisfy the symmetry requirementsp. 457
Perturbation theoryp. 459
The selection rulesp. 461
Appendicesp. 463
Values of some physical constantsp. 463
Energy conversion factorsp. 464
Further Readingp. 465
Indexp. 467
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780815340874
ISBN-10: 0815340877
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 352
Published: 21st February 2006
Publisher: Taylor & Francis Inc
Country of Publication: US
Dimensions (cm): 22.9 x 17.8  x 2.41
Weight (kg): 1.04
Edition Number: 1