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Martin Peschel
Martin Peschel
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Since the Operator $H_0$ is Hermitian, $\langle\psi_p|H_0|\chi\rangle$$\langle\phi_p|H_0|\chi\rangle$ is equal to its adjoint $\langle\chi|H_0|\psi_p\rangle^*$$\langle\chi|H_0|\phi_p\rangle^*$. Now, we act to the right, and since $E^{0}_p$$E^{(0)}_p$ is real, we obtain $E_p^0\langle\chi|\psi_p\rangle^*$$E_p^{(0)}\langle\chi|\phi_p\rangle^*$ which is equal to $E_p^0\langle \psi_p|\chi\rangle$$E_p^{(0)}\langle \phi_p|\chi\rangle$ since the unit operator is also hermitian.

Since the Operator $H_0$ is Hermitian, $\langle\psi_p|H_0|\chi\rangle$ is equal to its adjoint $\langle\chi|H_0|\psi_p\rangle^*$. Now, we act to the right, and since $E^{0}_p$ is real, we obtain $E_p^0\langle\chi|\psi_p\rangle^*$ which is equal to $E_p^0\langle \psi_p|\chi\rangle$ since the unit operator is also hermitian.

Since the Operator $H_0$ is Hermitian, $\langle\phi_p|H_0|\chi\rangle$ is equal to its adjoint $\langle\chi|H_0|\phi_p\rangle^*$. Now, we act to the right, and since $E^{(0)}_p$ is real, we obtain $E_p^{(0)}\langle\chi|\phi_p\rangle^*$ which is equal to $E_p^{(0)}\langle \phi_p|\chi\rangle$ since the unit operator is also hermitian.

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Martin Peschel
Martin Peschel
  • 377
  • 1
  • 7

Since the Operator $H_0$ is Hermitian, $\langle\psi_p|H_0|\chi\rangle$ is equal to its adjoint $\langle\chi|H_0|\psi_p\rangle^*$. Now, we act to the right, and since $E^{0}_p$ is real, we obtain $E_p^0\langle\chi|\psi_p\rangle^*$ which is equal to $E_p^0\langle \psi_p|\chi\rangle$ since the unit operator is also hermitian.