Wavefunction normalization.

Often the relative probability of finding an atom in its excited state at time t is given by |psi(t)|^2 ~ e^(-2t/T), where T is the lifetime of the excited state. Normalize this probability distribution, and when does the probability drop to half the maximum value?

Energy eigen states and wave functions of an infinite square well

Show a detailed derivation for the time independent Schroedinger Equation for an 1-d square well , symmetric about the origin, with a dimension of L (-L/2 to 0 to +L/2).

Schrodinger's Equation

A one-dimensional quantum well of width 19 nm is created, and measurements show that the energy difference between the ground state and the first excited state is 0.19 eV. What is the effective mass of the electron in the well? Answer in units of kg.

Spin Angular Monentum

(A)A particle with spin 1 has orbital angular momentum L_lowercase=0. What are the possible values for the total angular momentum Quantum number j? (B)The same particle has L_lowercase=3. What are the possible values for j? I need to know how to do a problem like this, detailed solution please.

A particle has spin 1, so that m_s =-1, 0 or 1. Derive the matrices which correspond to S_x, S_y and S_z.

A particle has spin 1, so that m_s=-1,0 or 1. Derive the matrices which correspond to S_x, S_y and S_z.