Quantum Mechanics In Three Dimensions NAT - IIT JAM MCQ

Find the level of degeneracy for particle in a 3d box with energy 

Find the value of the normalisation constant in the unit  of that normalizes the ground state wavefunction of the particle in a box of lengths L, 2L, 3L in  x, y and z directions respectively. Take  √3 = 1.732

Find the level of degeneracy for a 3 dimensional isotropic quantum harmonic oscillator of energy 

Consider two harmonic oscillators in 3 dimensions. For what ratio of angular frequencies will the first excited state of one oscillator have energy twice that of the second oscillator’s third excited state energy i.e find 

Modeling a defect trap in a crystal as a 3d box with edge length 5Å, find the values of energy for an electron bound to the defect site, assuming the electron to be in the ground state. (in eV)

Find the probability of finding a particle in a 3d box of length L, in the volume 

(Assume the particle to be in the ground state).

Calculate the probability that the electron in the ground state of hydrogen will be found outside the first Bohr radius in the unit e^–2. Take