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10 Nov 2019
We consider a particle in a two-dimensional square well with side a. The well lies in the (x - y) plane, as shown in the figure (the left panel shows a top-view of the well, and the right panel shows the well and particle in perspective.) Since the "motion" of the particle in the x direction is independent of its motion in the y direction, the spatial part of the wavefunction is separable. Thus, the generic wavefunction for the particle in the well is psi(x, y) = A sin nx pi x/a sin ny pi y/a, where nx and ny are positive integers. Normalize the wavefunction and find the constant A. Find a general expression for the energy of the particle as a function of the quantum numbers nx and ny.
We consider a particle in a two-dimensional square well with side a. The well lies in the (x - y) plane, as shown in the figure (the left panel shows a top-view of the well, and the right panel shows the well and particle in perspective.) Since the "motion" of the particle in the x direction is independent of its motion in the y direction, the spatial part of the wavefunction is separable. Thus, the generic wavefunction for the particle in the well is psi(x, y) = A sin nx pi x/a sin ny pi y/a, where nx and ny are positive integers. Normalize the wavefunction and find the constant A. Find a general expression for the energy of the particle as a function of the quantum numbers nx and ny.
Elin HesselLv2
20 Jul 2019