2-D Schrödinger equation
3-D Schrödinger equation
Eigenfunction solutions
Energy eigenvalues
Density of states
Energy spectral density
at zero temperature
Fermi energy EF
Internal energy
at zero temperature
Magnetization
at zero temperature
2-D Schrödinger equation | 3-D Schrödinger equation | ||||||
Eigenfunction solutions |
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Energy eigenvalues | $$E=\hbar \omega_c\left( \nu+ \frac{1}{2}\right) \pm \frac{g\mu_B}{2}B_z$$ $$E=\hbar \omega_c\left( \nu+ \frac{1}{2}\pm \frac{g}{4}\right) $$ $$\nu = 0,1,2,\cdots\qquad\omega_c=\frac{|eB_z|}{m}$$ | $$E=\hbar \omega_c\left( \nu+ \frac{1}{2}\right) + \frac{\hbar^2}{2m} k_{z}^2 \pm \frac{g\mu_B}{2}B_z$$ $$E=\hbar \omega_c\left( \nu+ \frac{1}{2}\pm \frac{g}{4}\right) + \frac{\hbar^2}{2m} k_{z}^2 $$ $$\nu = 0,1,2,\cdots\qquad\omega_c=\frac{|eB_z|}{m}$$ | |||||
Density of states |
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Energy spectral density |
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Fermi energy EF |
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Internal energy |
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Magnetization |
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