Draw an energy level diagram for a. nonrelativistic particle confined inside a three-dimensional cube-shaped box, showing all states with energies below 15. (h2/8mL2 ) . Be sure to show each linearly independent state separately, to indicate the degeneracy of each energy level. Does the average number of states per unit energy increase or decrease as E increases?
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The energy for a non relativistic particle in a three dimensional box is
Where, = Planck’s constant , is the mass of the particle, is the length of the cubic box ,\
All states with energies below 15 are as follows
For () = (1,1,1) the energy of the particle is
For () = (1,1,2) (1,2,1) (2,1,1) the energy of the particle is
For () = (1,2,2) (2,1,2) (2,2,1) the energy of the particle iss
For () = (1,1,3) (1,3,1) (3,1,1) the energy of the particle is
For () = (2,2,2) the energy of the particle is
For () = (1,2,3) (1,3,2) (2,1,3) (2,3,1) (3,1,2) (3,2,1) the energy of the particle is
is as shown in the fig.