Using quantum theory derivation and numerical calculation methods，the diagram
and model
of one- dimensional potential box function are firstly obtained. Then the
wave function，energy
level and probability density of N-dimensional potential box functions in
quantum mechanics are
studied comprehensively and systematically. Fi- nally，all characteristics
of the potential box
functions are simulated using MATLAB software. We find that the ener- gy of
particles is quantized
and discontinuous in N-dimensional potential box. The quantum number n
cannot be ze- ro，and the
higher the quantum number n is，the higher the energy level is，while the
higher the mass
m is，the lower the energy level is. Generally，the larger one-dimensional
potential box length a
is，the lower the correspond- ing energy level is. The number of nodes is
N-1，and the more
the nodes are，the shorter the wavelength is，the higher the frequency is，the
higher the energy
level is. For two-dimensional potential box function，the number of peaks is
nₓ ×ny ，and the
intersection numbers of wave function and a plane of Ψ = 0 is nₓ ×ny ，too.
For degeneracy， in
general，the degeneracy of particles in the two-dimensional potential box
model is uncertain. But
for the two di- mensional square potential box function model，the energy
level degeneracy of the
particles in the box can be divid- ed into general and special cases. The
degeneracy of
three-dimensional potential box function are nx +ny +nz . The vi-
sualization results are in
complete agreement with the theoretical results. Finally，the color function
of MATLAB
software is firstly used to realize the four-dimensional representation，and
the four-dimensional
slice diagram of the three-dimensional potential box function are obtained.
The results of
this visualization are in complete agreement with the theoretical
results，and it is also of
great significance for the understanding of the abstract concept.
Just Accepted
