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I've noticed that some professors will jump between second quantized creation/annihilation operators and wavefunctions rather easily. For instance [itex] \Psi_k \propto c_k + ac_k^{\dagger}[/itex] with "a" some constant (complex possibly). I'm fairly familiar with the second quantized notation, and from my understanding the concept of wavefunctions is essentially abandoned. The creation/annihilation operators simply add a particle into a state in the number basis. So what would be the way to "translate" some single particle wavefunciton [itex] \Psi_k [/itex] into second quantization, and what would the method/reasoning be?

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# I Creation operator and Wavefunction relationship

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