Abstract:
Based on quantum theory and numerical calculation, we have mainly studied the basic characteristic of
n-dimensional linear harmonic oscillator, including wave function, energy, energy levels, degeneracy and probability density, and obtain four-dimensional figures of three-dimensional harmonic oscillator and 3D figures of two-dimensional harmonic oscillator. The results show that the energy of a linear harmonic oscillator is discrete and the energy is quantized. The energy of a harmonic oscillator is evenly distributed, two adjacent energy level spacing is Δ
E=
ħω. The degeneracy of two-dimensional linear harmonic oscillator is
N+1, but the corresponding ground-state wave function has no degeneracy when
N=0. The intersection line between wave function and the plane with Ψ = 0 is N. The probability density graph can more intuitively show the number and magnitude of the peak value of probability density, and the number of maximal value of probability density distribution is (
nx+1)(
ny+1). For the three-dimensional linear harmonic oscillator, based on the ground state wave function, within a certain range (−3 ,3), the slices numbers of the
x,
y and
z axis are
nx+1,
ny+1,
nz+1, respectively. The total number of slices is
nx+
ny+
nz+3. In addition, this research has obtained the four-dimensional space slice diagrams of three-dimensional linear harmonic oscillator by MATLAB software. The results of this visualization have established consistence with the theoretical results.