Quantum Mechanics

[edit] Qualifier-type questions

Derive the constants for a harmonic osciallator from first principles starting with the given trial wavefunction

Given a Hamiltonian in matrix form and an inital condition, solve for the time evolution of the state vector

Given an inital wavefunction in an infinite square well, convert it to the standard basis functions

A perturbation is applied to a wavefunction, what are first and second order corrections to the energy?

Consider a spinless QM particle in magnetic field $\vec B = B_0 \hat z$ with a symmetric gauge in a scalar potential. What is the Hamiltonian?

A particle in a central potential has an orbital angular momentum l = $2\hbar$ and a spin $s = 1\hbar$ . Find the energy

levels and degeneracies associated with a spin-orbit interaction term $H_i = AL \cdot S$ .

A Ping pong in Hong Kong is bounced while in its ground state. So what?

A particle in a uniform electrostatic E field, how classical is it?

Name some of the famous experiments in quantum mechanics and a brief description of their importance

A small collection of GRE problems/solutions