Quantum Mechanics for graduates - Exercises

The pool contains solutions by students. The solutions are not "ideal": some are non-efficient; and possibly there are some non-critical errors and typos. We hope to improve the solutions in future cycles. Note that ex 1025, 4828, 4850 are taken from the QM exercise pool of the undergraduate course.

ex_1000   [link]   [gate]   [forum]   Math
ex_1210   [link]   [gate]   [forum]   (1210) Fourier transforms - generalized functions
ex_1230   [link]   [gate]   [forum]   (1230) Fourier transforms - theorems
ex_1240   [link]   [gate]   [forum]   (1240) Gaussian integrals
ex_1250   [link]   [gate]   [forum]   (1250) Wigner function for a Gaussian wavepacket
ex_1251   [link]   [gate]   [forum]   (1251) Winger function of a particle in a box
ex_1252   [link]   [gate]   [forum]   (1252) Wigner function for superposition of Gaussians
ex_2300   [link]   [gate]   [forum]   Transformations of the Hamiltonian
ex_2331   [link]   [gate]   [forum]   (2331) Transformations - moving box
ex_2332   [link]   [gate]   [forum]   (2332) Transformations - accelarating box 2008
ex_2336   [link]   [gate]   [forum]   (2336) Transformations - Box with moving wall 2006
ex_2552   [link]   [gate]   [forum]   (2552) מטריצת פיזור של צומת
ex_8000   [link]   [gate]   [forum]   The propagator and the Green function
ex_8114   [link]   [gate]   [forum]   (8114) Propagator for a particle in uniform field
ex_8150   [link]   [gate]   [forum]   (8150) Propagator for Hard wall
ex_8160   [link]   [gate]   [forum]   (8160) Propagator for soft wall 2008
ex_8171   [link]   [gate]   [forum]   (8171) Propagator in a circle
ex_8172   [link]   [gate]   [forum]   (8172) Propagator in a box
ex_8210   [link]   [gate]   [forum]   (8210) Extracting spectrum from the propagator
ex_8212   [link]   [gate]   [forum]   (8212) Correlator for free particle
ex_8230   [link]   [gate]   [forum]   (8230) Getting eigenstates from the Resolvent
ex_8330   [link]   [gate]   [forum]   (8330) Getting matrix elements via boundary integral
ex_8360   [link]   [gate]   [forum]   (8360) Reolvent for particle with linear dispersion relation 2009
ex_8370   [link]   [gate]   [forum]   (8370) Reolvent of particle in a box
ex_8500   [link]   [gate]   [forum]   Formal perturbation theory
ex_8512   [link]   [gate]   [forum]   (8512) Gamow decay from a deep box via a delta barrier
ex_8520   [link]   [gate]   [forum]   (8520) Decay from a two-level-system 2005
ex_8521   [link]   [gate]   [forum]   (8521) Decay from an aymmetric double well
ex_8530   [link]   [gate]   [forum]   (8530) Decay form a ring 2006
ex_8540   [link]   [gate]   [forum]   (8540) Deacy from 3 sites 2007
ex_8550   [link]   [gate]   [forum]   (8550) Decay in misc geometries
ex_9000   [link]   [gate]   [forum]   Scattering theory
ex_9010   [link]   [gate]   [forum]   (9010) Scattering by cubic lattice
ex_9011   [link]   [gate]   [forum]   (9011) Scattering from a dipole
ex_9012   [link]   [gate]   [forum]   (9012) Scattering from a disc - Poisson Spot
ex_9020   [link]   [gate]   [forum]   (9020) Scattering by inverse cosh
ex_9030   [link]   [gate]   [forum]   (9030) Scattering on delta-barrier in 1D conduction band
ex_9040   [link]   [gate]   [forum]   (9040) Scattering on widened delta-barrier in 1D conduction band
ex_9050   [link]   [gate]   [forum]   (9050) Scattering on delta-scatterer in 3D conduction band
ex_9060   [link]   [gate]   [forum]   (9060) Optical theorem 2D 2005
ex_9100   [link]   [gate]   [forum]   Scattering [1D]
ex_9120   [link]   [gate]   [forum]   (9120) Scattering matrix for quantum dot with two leads
ex_9121   [link]   [gate]   [forum]   (9121) Scattering phase shift for quantum dot with one lead
ex_9130   [link]   [gate]   [forum]   (9130) Scattering phase shift for single lead with attached quantum dot 2010
ex_9180   [link]   [gate]   [forum]   (9180) Scattering by delta in waveguide
ex_9190   [link]   [gate]   [forum]   (9190) Inelastic scattering by delta
ex_9200   [link]   [gate]   [forum]   Scattering [3D]
ex_9220   [link]   [gate]   [forum]   (9220) Maximal cross section of a sphere
ex_9230   [link]   [gate]   [forum]   (9230) Scattering by a very small sphere
ex_9250   [link]   [gate]   [forum]   (9250) Phase shifts for 1/r^2 scattering 2007
ex_9260   [link]   [gate]   [forum]   (9260) Phase shifts for a sphere
ex_9270   [link]   [gate]   [forum]   (9270) Phase shifts for a shielded sphere [matching procedure]
ex_9272   [link]   [gate]   [forum]   (9272) Phase shifts for a spherical shell [Lippman-Schwinger]
ex_9280   [link]   [gate]   [forum]   (9280) Resonances of a shielded spherical well 2009
ex_9290   [link]   [gate]   [forum]   (9290) Resonances of an hollow spherical shell 2005
ex_9300   [link]   [gate]   [forum]   Scattering [3D, Born]
ex_9330   [link]   [gate]   [forum]   (9330) Derivation of Born for phase shift in spherical geometry via T-matrix
ex_9332   [link]   [gate]   [forum]   (9332) Resonance cross section in spherical geometry via T-matrix
ex_9350   [link]   [gate]   [forum]   (9350) Born approximation for scattering from a spherical shell
ex_9355   [link]   [gate]   [forum]   (9355) Based on Born find radial potential for getting constant phase shift
ex_9400   [link]   [gate]   [forum]   Quantum fields
ex_9420   [link]   [gate]   [forum]   (9420) Casimir Effect
ex_9500   [link]   [gate]   [forum]   Many body systems
ex_9520   [link]   [gate]   [forum]   (9520) Fock space language - expressions for operators
ex_9527   [link]   [gate]   [forum]   (9527) Electrons interacting with bosonic bath
ex_9630   [link]   [gate]   [forum]   (9630) Bose Hubbard for two sites - spin language
ex_9636   [link]   [gate]   [forum]   (9636) Bose-Hubbard model - energy of SF/ST/MI states
ex_9637   [link]   [gate]   [forum]   (9637) Fermi-sea energy including Coulomb interaction
ex_9710   [link]   [gate]   [forum]   (9710) Two particles in two sites with interaction
ex_9720   [link]   [gate]   [forum]   (9720) Hubbard model with two sites
ex_9722   [link]   [gate]   [forum]   (9722) Electrons in atomic orbitals - exchange
ex_9724   [link]   [gate]   [forum]   (9724) Electrons in atomic orbitals - Hund laws
ex_9730   [link]   [gate]   [forum]   (9730) Anderson impurity model
ex_9740   [link]   [gate]   [forum]   (9740) Kondo scattering
ex_9750   [link]   [gate]   [forum]   (9750) Bose-Hubbard model - excitations
ex_9751   [link]   [gate]   [forum]   (9751) Bogolyubov transformation for Bosons - one or two sites
ex_9752   [link]   [gate]   [forum]   (9752) Bogolyubov transformation for fermions - two sites
ex_9753   [link]   [gate]   [forum]   (9753) Bosonic bath mode
ex_9754   [link]   [gate]   [forum]   (9754) Fermions that are coupled to a bath of bosons
ex_9755   [link]   [gate]   [forum]   (9755) Bogolyubov transformation for fermions - Kitaev chain
ex_9756   [link]   [gate]   [forum]   (9756) Bogolyubov transformation for Fermions - XY model
ex_9800   [link]   [gate]   [forum]   Interaction with the EM field
ex_9810   [link]   [gate]   [forum]   (9810) Hamiltonian of electron in EM field
ex_9820   [link]   [gate]   [forum]   (9820) Two-level-atom emission - radiance and superradiance
ex_9821   [link]   [gate]   [forum]   (9821) Hydrogen decay rate from 2p to 1s
ex_9830   [link]   [gate]   [forum]   (9830) Two-level-atoms emission - superradiance