- #1
Mimb8
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Particle Number Operator (Hermitian??)
Hey guys,
I'm studying the quantic harmonic oscillator and I'm using "Cohen-Tannoudji Quantum Mechanics Volume 1".
At some point he introduced the particle number operator, N, such that:
N=a+.a , where a+ is the conjugate operator of a.
The line of proof that they used to show that N is hermitian is the following:
N+=a+.(a+)+=N , where N+ is the conjugate operator of N.
Somehow, in ways I cannot understand, this proves it.
But everytime I try and prove it myself I get to the conclusion that N is not hermitian.
Can someone be kind enough and help me with this :)
Thank you
Hey guys,
I'm studying the quantic harmonic oscillator and I'm using "Cohen-Tannoudji Quantum Mechanics Volume 1".
At some point he introduced the particle number operator, N, such that:
N=a+.a , where a+ is the conjugate operator of a.
The line of proof that they used to show that N is hermitian is the following:
N+=a+.(a+)+=N , where N+ is the conjugate operator of N.
Somehow, in ways I cannot understand, this proves it.
But everytime I try and prove it myself I get to the conclusion that N is not hermitian.
Can someone be kind enough and help me with this :)
Thank you