Short lecture on the three-dimensional particle in a box.
The three dimensional particle in a box has a Hamiltonian which can be factored into an independent function of the x, y, and z directions. Thus, we can use separation of variables to express the wave function as a product of three one-dimensional wavefunctions, and solve three individual Schrodinger equations for each dimension. The energy is then a sum of the energy in each dimension. Each dimension has its own quantum number (nx, ny, and nz) all of which can take on any integer value from one to infinity.
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