An electron of mass me is trapped in a two-dimensional infinite square potential well. The potential inside the well is zero, and the widths of the well are L and 2L along the x-axis and y-axis, respectively. The electron is in an excited state and its wave function, with reference to a Cartesian coordinate system having its origin located at one of the corners of the well, is given as:

1. ???Find the expectation value of the total energy of the electron. (ans: 5?^2pi^2/(2mL^2))
2. ???How much energy will be released when the electron relaxes back to the ground state.(ans: -15?^2pi^2/(8mL^2))

Give your results in terms of me, L, it and h.

5. An electron of mass me is trapped in a two-dimensional innite square potential well. The potential inside the well is zero, and the widths of the well are L and 2L along the xaxis and yaxis, respectively. The electron is in an excited state and its wave function, with reference to a Cartesian coordinate system having its origin located at one of the corners of the well, is given as: 111(x, y) = B sinyix sin zfy a) Find the expectation value of the total energy of the electron. b) How much energy will be released when the electron relaxes back to the ground state. Give your results in terms of me, L, TE and ft. (12 marks)