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Display information for equation id:math.1703.38 on revision:1703

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\begin{align}

& \hat{H}={{{\hat{H}}}_{B}}\times 1+{{H}_{S}}=\left[\frac{1}{2{{m}_{0}}}{{\left( \bar{p}-e\bar{A} \right)}^{2}}+V(r) \right]\times 1-\frac{\left| e \right|\hbar B}{2{{m}_{0}}}{{{\hat{\bar{\sigma }}}}_{3}} \\
& \hat{H}\cong \left[\frac{{{{\bar{p}}}^{2}}}{2{{m}_{0}}}+V(r) \right]\times 1-\frac{\left| e \right|B}{2{{m}_{0}}}\left( {{{\hat{L}}}_{3}}\times 1+\hbar {{{\hat{\bar{\sigma }}}}_{3}} \right) \\
& \frac{{{{\bar{p}}}^{2}}}{2{{m}_{0}}}+V(r)={{H}_{0}} \\
& {{H}_{0}}\left| nlm \right\rangle ={{E}_{nl}}\left| nlm \right\rangle \\
\end{align}

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H ^ = H ^ B × 1 + H S = [ 1 2 ⁢ m 0 ⁢ ( p ¯ - e ⁢ A ¯ ) 2 + V ⁢ ( r ) ] × 1 - | e | ⁢ ℏ ⁢ B 2 ⁢ m 0 ⁢ σ ¯ ^ 3 H ^ ≅ [ p ¯ 2 2 ⁢ m 0 + V ⁢ ( r ) ] × 1 - | e | ⁢ B 2 ⁢ m 0 ⁢ ( L ^ 3 × 1 + ℏ ⁢ σ ¯ ^ 3 ) p ¯ 2 2 ⁢ m 0 + V ⁢ ( r ) = H 0 H 0 ⁢ | n ⁢ l ⁢ m ⟩ = E n ⁢ l ⁢ | n ⁢ l ⁢ m ⟩ absent ^ 𝐻 subscript ^ 𝐻 𝐵 1 subscript 𝐻 𝑆 delimited-[] 1 2 subscript 𝑚 0 superscript ¯ 𝑝 𝑒 ¯ 𝐴 2 𝑉 𝑟 1 𝑒 Planck-constant-over-2-pi 𝐵 2 subscript 𝑚 0 subscript ^ ¯ 𝜎 3 missing-subexpression ^ 𝐻 delimited-[] superscript ¯ 𝑝 2 2 subscript 𝑚 0 𝑉 𝑟 1 𝑒 𝐵 2 subscript 𝑚 0 subscript ^ 𝐿 3 1 Planck-constant-over-2-pi subscript ^ ¯ 𝜎 3 missing-subexpression superscript ¯ 𝑝 2 2 subscript 𝑚 0 𝑉 𝑟 subscript 𝐻 0 missing-subexpression subscript 𝐻 0 ket 𝑛 𝑙 𝑚 subscript 𝐸 𝑛 𝑙 ket 𝑛 𝑙 𝑚 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle\hat{H}={{{\hat{% H}}}_{B}}\times 1+{{H}_{S}}=\left[\frac{1}{2{{m}_{0}}}{{\left(\bar{p}-e\bar{A}% \right)}^{2}}+V(r)\right]\times 1-\frac{\left|e\right|\hbar B}{2{{m}_{0}}}{{{% \hat{\bar{\sigma}}}}_{3}}\\ &\displaystyle\hat{H}\cong\left[\frac{{{{\bar{p}}}^{2}}}{2{{m}_{0}}}+V(r)% \right]\times 1-\frac{\left|e\right|B}{2{{m}_{0}}}\left({{{\hat{L}}}_{3}}% \times 1+\hbar{{{\hat{\bar{\sigma}}}}_{3}}\right)\\ &\displaystyle\frac{{{{\bar{p}}}^{2}}}{2{{m}_{0}}}+V(r)={{H}_{0}}\\ &\displaystyle{{H}_{0}}\left|nlm\right\rangle={{E}_{nl}}\left|nlm\right\rangle% \\ \end{aligned}}}

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H^=H^B×1+HS=[12m0(p¯−eA¯)2+V(r)]×1−|e|ℏB2m0σ¯^3H^≅[p¯22m0+V(r)]×1−|e|B2m0(L^3×1+ℏσ¯^3)p¯22m0+V(r)=H0H0|nlm⟩=Enl|nlm⟩

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