- #1

kuan

- 10

- 0

Dear All,

I am right now facing a problem of the adjoint operator.

From the mathematical point of view, if [tex] T [/tex] is a linear operator mapping from Hilbert space [tex] H [/tex] to another Hilbert space [tex] H' [/tex], there exist an unique adjoint operator [tex] T^{\dagger} [/tex] mapping from [tex] H' [/tex] back to [tex] H [/tex].

However I am right now struggling in understanding the physical meaning of the adjoint operator (not necessarily self-adjoint). The only thing I can think is that the operator [tex] T [/tex] and [tex] T^{\dagger}[/tex] have the same eigenvalues. Does this reveals some kind of symmetry? Could some one give me a bit hint for that?

Many thanks

I am right now facing a problem of the adjoint operator.

From the mathematical point of view, if [tex] T [/tex] is a linear operator mapping from Hilbert space [tex] H [/tex] to another Hilbert space [tex] H' [/tex], there exist an unique adjoint operator [tex] T^{\dagger} [/tex] mapping from [tex] H' [/tex] back to [tex] H [/tex].

However I am right now struggling in understanding the physical meaning of the adjoint operator (not necessarily self-adjoint). The only thing I can think is that the operator [tex] T [/tex] and [tex] T^{\dagger}[/tex] have the same eigenvalues. Does this reveals some kind of symmetry? Could some one give me a bit hint for that?

Many thanks

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