Consider a spinless particle of mass, M which is moving in a 3-dimensional potential  V(x, y, z) = {1/2 mw^2z^2,0

Consider a spinless particle of mass, M which is moving in a 3-dimensional potential 

V(x, y, z) = {^{1/2 mw^2z^2,0<x<a, 0<y<b.} _{infinity, otherwise} 

_{Obtain the total energy and tge total wavefuction for this particle. Assume that in addition to tge potential V(x, y, z)  this particle also has a negative electric charge -q and that is subjected to a constant electric field £ directed along the z-axis. Derive the energy expressions} E_{nz for this particle and also its total energy} E_{nz ny nx. Hence find the energies of ground state and the first excited state}