- #1

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## Main Question or Discussion Point

if I derive a hermitian relation

use:

[1] [tex]\left \langle \Psi _{m} | H |\Psi _{n}\right \rangle =E_{n}\left \langle \Psi _{m} |\Psi _{n}\right \rangle[/tex]

and

[2] [tex]\left \langle \Psi _{n} | H |\Psi _{m}\right \rangle =E_{m}\left \langle \Psi _{n} |\Psi _{m}\right \rangle[/tex]

if i take the complex conjugate of [2]

[3] [tex]\left \langle \Psi _{m} | H^{*} |\Psi _{n}\right \rangle =E_{m}\left \langle \Psi _{m} |\Psi _{n}\right\rangle[/tex]

then [3] - [1] i get

[tex]H_{mn}^{*} - H_{mn} = 0[/tex]

therefore

[tex]H_{mn}^{*} = H_{mn}[/tex]

[tex]H_{nm}^{*} = H_{mn}[/tex]

so does

[tex]H_{nm}^{*} = H_{mn}^{*} [/tex] ? and when i took the complex conjugate was that result correct, i'm getting a little confused with notation.

thanks in advance for any guidance.

use:

[1] [tex]\left \langle \Psi _{m} | H |\Psi _{n}\right \rangle =E_{n}\left \langle \Psi _{m} |\Psi _{n}\right \rangle[/tex]

and

[2] [tex]\left \langle \Psi _{n} | H |\Psi _{m}\right \rangle =E_{m}\left \langle \Psi _{n} |\Psi _{m}\right \rangle[/tex]

if i take the complex conjugate of [2]

[3] [tex]\left \langle \Psi _{m} | H^{*} |\Psi _{n}\right \rangle =E_{m}\left \langle \Psi _{m} |\Psi _{n}\right\rangle[/tex]

then [3] - [1] i get

[tex]H_{mn}^{*} - H_{mn} = 0[/tex]

therefore

[tex]H_{mn}^{*} = H_{mn}[/tex]

**BUT**in my notes its given as[tex]H_{nm}^{*} = H_{mn}[/tex]

so does

[tex]H_{nm}^{*} = H_{mn}^{*} [/tex] ? and when i took the complex conjugate was that result correct, i'm getting a little confused with notation.

thanks in advance for any guidance.