Question

For a quantum particle confined inside a cubic box of side l, the ground state energy is given by e0. The energy of the first excited state is

Answer 1

The energy of a quantum particle confined in a cubic box in its first excited state is equal to π²h²/8mL².

• By solving the Schrodinger's wave equation: HΨ = EΨ for a cubical box of length L, we obtain E(nx,ny,nz)= (π²h²/8mL²)×(nx²+ny²+nz²).
• For ground state (nx,ny,nz)=(0,0,0) , hence E=0
• For first excited state their exists three degenerate energy levels corresponding to (nx,ny,nz) equal to (1,0,0) , (0,1,0) and (0,0,1).
• Therefore energy of first excited state is equal to π²h²/8mL².