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siniylev [52]
3 years ago
6

Problems that require solving the three-dimensional schrödinger equation can often be reduced to related one-dimensional problem

s. an example of this would be the particle in a cubical box. consider a cubical box with rigid walls (i.e., u(x,y,z)=∞ outside of the cube) and edges of length l. the general solution for this problem is
Mathematics
1 answer:
dusya [7]3 years ago
8 0
The wavefunction for a particle in a one-dimension box is a well-known problem, which has as a solution:

Ψ(x) = √(2/l) sin (nπx/l)

When the box has three dimensions, the general solution is simply the multiplication of the solutions for each dimension, therefore:

Ψ(x) = K · sin (n_x·π·x / l) · sin (n_y·π·y / l) · sin <span>(n_z·π·z / l)</span>
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