Answer to Question #6031 in Quantum Mechanics for Grzegorz Mazur

Question

Find wave functions of the states of a particle in a harmonic oscillator potential
that are eigenstates of Lz operator with eigenvalues -1 h , 0, 1 h and have smallest possible eigenenergies. Check whether these states are also the eigenstates of L^2 operator. Eventually, write the wave functions using spherical coordinates and normalize independently
their radial and angular parts.