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Vydání první

Praha : MatfyzPress, nakladatelství Matematicko-fyzikální fakulty Univerzity Karlovy, 2021

246 stran : ilustrace (některé barevné) ; 24 cm

ISBN 978-80-7378-436-2 (brožováno)

Odborná edice MatfyzPress

Nad názvem: Matematicko-fyzikální fakulta, Univerzita Karlova

Obsahuje bibliografii na stranách 245-246 a rejstřík

001640568

I. Variational Methods 9 // A. Introduction 9 // B. Linear harmonic oscillator with a Gaussian test function 11 // C. The first excited state of a linear harmonic oscillator 14 // D. Linear harmonic oscillator with test function 1/(1 + x2) 16 // E. Hydrogen atom with a Gaussian test function 18 // F. Particle in a -r-3/2 potential 21 // G. No matrix element, no fun 24 // H. Quantum rotor with an A cos2 Ń„ perturbation 26 // II. Time-Independent Perturbation Theory 31 // A. Introduction 31 // B. Linear harmonic oscillator with an Ax6 potential 32 // C. Square well potential with an Ax2 perturbation 34 // D. Linear harmonic oscillator with a modified potential 35 // E. Cubic anharmonic oscillator 39 // F. Particle in a periodic box and with a step potential 41 // G. Particle in a periodically repeated box with a Dirac б perturbation 43 // H. The double-well quadratic potential 48 // I. A ramp-like infinite square well 50 // J. Don’t step on the pin! 53 // K. A pothole-like infinite square well 55 // L The bound state in an external electric field 56 // M. Linear harmonic oscillator with an Ax2y2 perturbation 59 // N. Hydrogen atom in an electric field. The Stark effect in hydrogen 64 // 0. The perturbed Hamiltonian matrix for degenerate states 69 // P. Dipole in an electric field 76 // III. Time-Dependent Problems 85 // A. Introduction 85 // B. /Đ—-decay of tritium 86 // C. A charged particle in a 3D box with an electric field 93 D. Hydrogen atom in a time-dependent electric field 105 // E. Time-dependent force acting on a linear harmonic oscillator 108 // F. Time-dependent electric field 113 // G. Time evolution of a system with coupled states 117 //

IV. Angular Momentum 125 // A. Introduction 125 // B. Expectation values of Lx and operators 126 // C. Measurement of spin along a rotated axis 128 // D. Angular momentum after passing through a Stern-Gerlach // apparatus 131 // A // E. Eigenstates of Lx 135 // F. Two non-interacting spins 137 // G. Spin-orbit interaction 139 // H. Coupling of momenta 140 // 1. Lowering operators 144 // J. Spin-spin Hamiltonian 145 // K. Matrix representation of the spin-spin Hamiltonian 147 // L. Zeeman effect on hyperfine splitting in hydrogen 149 // V. Miscellaneous 155 // A. Introduction 155 // B. Lower-bounded spectrum of a linear harmonic oscillator 155 // C Superposition of states of a linear harmonic oscillator 157 // D. The uncertainty principle 159 // E. Ehrenfest’s theorem 160 // F. The virial theorem 162 // G. Detection of (in)distinguishable particles 164 // H. The polarization density matrix in 2 x 2 space 171 // I. Helium ground state energy I: Variational principle 175 // J. Helium ground state energy II: First-order perturbation theory 182 // K. Optical selection rules 186 // L. Rotational selection rules 193 // M. The Hubbard model 203 // N. Analytic properties of Bloch functions 212 // Appendix A. Simple Quantum Systems 217 // I. Quantum harmonic oscillator 217 // a. Hamiltonian and eigenstates 217 // b. Ladder operators 218 // c. Integrals 219 // d. Gaussian integrals 221 // 2. Particle in an infinitely deep square well potential 223 // a. Hamiltonian and eigenstates 223 // b. Integrals 224 // 3. Quantum rotor 228 // a. Hamiltonian and eigenstates 228 // b. Integrals 229 // 4. 2D quantum rotor 230 // a. Hamiltonian and eigenstates 230 // b. Integrals 231 // 5. Hydrogen atom 233 // a. Integrals 234 // Appendix B. Gamma Function 235 // Appendix C. Physical Constants 236 // Appendix D. Conversion Factors 239