Calculate the reflection probability of a particle with a kinetic energy of Ekin = 4 eV at a negative potential step of height Eo = -12 eV starting from the time-independent Schrödinger equation.

Use the time-dependent Schroedinger equation to calculate the period (in seconds) of the wavefunction for a particle of mass 9.109×10−31 kg in the ground state of a box of width 1.2×10−10 m.

An electron is trapped in an infinitely deep one-dimensional well of width 10 nm. Initially, the electron occupies the n = 4 state. Suppose the electron relaxes to ground state with the accompanying emission of a photon. Calculate the energy of the photon.

Show that the following function Y(0,9)= sin 0 cos e eiº is the solution of Schrödinger 1 1 equation: sin 0 21 sin 0 00 Y(0,0)= EY (0,9) and find the sin 0 dp? energy, E.