Note on a less ad hoc derivation of the second quantization formalism

TL;DR

This paper presents a clearer, more natural derivation of the second quantization formalism in quantum mechanics, emphasizing the equivalence between antisymmetric many-fermion states and Fock states, aimed at improving educational clarity.

Contribution

It offers a less ad hoc derivation of second quantization from first principles, avoiding reliance on harmonic oscillators and using fermion state equivalence.

Findings

Provides a transparent derivation method

Clarifies the connection between many-fermion states and Fock states

Enhances pedagogical approach to quantum mechanics

Abstract

Second quantization is an essential topic in senior undergraduate and postgraduate level Quantum Mechanics course. However, it seems that there is a lack of transparent and natural derivation of this formalism from the first-quantization one in most existing textbooks. Without introducing the concept of a simple harmonic oscillator and taking the case of an assembly of identical fermions as an example, we provide a less ad hoc derivation of the second quantization formalism based on the equivalence of the fully antisymmetric many-fermion states and the Fock states.