Reference no: EM132423740
Problem: Consider a cubic box, i.e. an innite well in 2 dimensions. Each side has length L. The energy eigenstates are labeled by quantum numbers (nx, ny).
Required:
Question 1: Could you help me write down the Hamiltonian of the system in cartesian coordinates.
Question 2: Could you help me write down the wavefunction for a (nx, ny) state, showing that it is an eigenfunction of the Hamiltonian.
Question 3: Calculate the energy Enx,ny of the (nx, ny) state.
Question 4: Write down the wavefunction and the energy for the ground state of this system.
Question 5: Is the state (nx, ny) = (5, 1) degenerate? If yes could you help me write down the energy and the corresponding eigenfunctions.
Question 6: What happens to the state (nx, ny) = (5, 1) if the length of one side of the box were increased by 5%?
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