Quantum

Derivation of Thomas-Reiche-Kuhn sum rules for position operator.

Computing hydrogen wave function with little information to remember.

Derivation of Thomas-Reiche-Kuhn sum rules for position operator.

We use the variational principle to prove that one-dimensional attractive potential of any shape supports a bound state.

We use the Born approximation to compute the differential cross section for the elastic scattering of a fast electron by a hydrogen atom in the ground state. We will treat the hydrogen atom as a fixed target with a time-independent charge …

Some fun with two dimensional harmonic oscillator with perturbation

A proof that square of the angular momentum vector is a Hermitian operator.

We show that if there is a simultaneous eigenstate of two components of the angular momentu, then this state has zero eigenvalues for all components.

Some fun with adding up angular momentum.

Finding eigenstates of spin projection operator.