- #1
Petar Mali
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[tex]\langle\hat{S}^z\rangle=\hbar\frac{(S-P_S)(1+P_S)^{2S+1}+(1+S+P_S)P_S^{2S+1}}{(1+P_S)^{2S+1}-P_S^{2S+1}}[/tex]
Can you tell me something more about Callen result? And this function [tex]P_S[/tex]?
In book Nolting "Quantum theory of magnetism" this relation is get from diferential equation
[tex]\frac{d^2\Omega}{d\alpha^2}+\frac{(1+P_S)+P_Se^{-a\hbar}}{(1+P_S)-P_Se^{-a\hbar}}\hbar\frac{d\Omega}{d\alpha}-\hbar^2S(S+1)\Omega=0[/tex]
two boundary conditions are
[tex]\Omega(0)=1[/tex]
and
[tex]\prod^{S}_{m_S=-S}(\frac{d}{d\alpha}-\hbar m_S)\Omega(\alpha)|_{\alpha=0}=0[/tex]
How he get this diferential equation?
Can you tell me something more about Callen result? And this function [tex]P_S[/tex]?
In book Nolting "Quantum theory of magnetism" this relation is get from diferential equation
[tex]\frac{d^2\Omega}{d\alpha^2}+\frac{(1+P_S)+P_Se^{-a\hbar}}{(1+P_S)-P_Se^{-a\hbar}}\hbar\frac{d\Omega}{d\alpha}-\hbar^2S(S+1)\Omega=0[/tex]
two boundary conditions are
[tex]\Omega(0)=1[/tex]
and
[tex]\prod^{S}_{m_S=-S}(\frac{d}{d\alpha}-\hbar m_S)\Omega(\alpha)|_{\alpha=0}=0[/tex]
How he get this diferential equation?
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