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- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_(Chong)/04%3A_Identical_Particles/4.03%3A_Second_QuantizationIn the usual tensor product notation, symmetric and antisymmetric states become quite cumbersome to deal with when the number of particles is large. We will now introduce a formalism called second qua...In the usual tensor product notation, symmetric and antisymmetric states become quite cumbersome to deal with when the number of particles is large. We will now introduce a formalism called second quantization, which greatly simplifies manipulations of such multi-particle states. (The reason for the name “second quantization” will not be apparent until later; it is a bad name, but one we are stuck with for historical reasons.)
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/08%3A_Identical_Particles/8.02%3A_Creation_and_Annihilation_OperatorsA particularly powerful way to implement the description of identical particles is via creation and annihilation operators.
- https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Book%3A_Thermodynamics_and_Statistical_Mechanics_(Arovas)/05%3A_Noninteracting_Quantum_Systems/5.09%3A_Appendix_I-_Second_QuantizationFor a one-body operator such as \HT, we have \[\begin{aligned} \expect{\alpha\ns_1\cdots\,\alpha\ns_N}{\HT}{\alpha'_1\cdots\,\alpha'_N} &=\int\!d^d\!x\ns_1\cdots\!\int\!d^d\!x\ns_N\> \Big(\prod_\a...For a one-body operator such as \HT, we have \[\begin{aligned} \expect{\alpha\ns_1\cdots\,\alpha\ns_N}{\HT}{\alpha'_1\cdots\,\alpha'_N} &=\int\!d^d\!x\ns_1\cdots\!\int\!d^d\!x\ns_N\> \Big(\prod_\alpha n\ns_\alpha!\Big)^{-1/2}\Big(\prod_\alpha n'_\alpha!\Big)^{-1/2} \times \\ &\hskip 0.5in \sum_{\sigma\in S\ns_N} (\pm 1)^\sigma\vphi^*_{\alpha\ns_{\sigma(1)}}(\Bx\ns_1)\cdots \vphi^*_{\alpha\ns_{\sigma(N)}}(\Bx\ns_N) \>\sum_{k=1}^N \HT\ns_i \>\vphi\ns_{\alpha'_{\sigma(1)}}(\Bx\ns_1)\cdots \vph…
- https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Nuclear_and_Particle_Physics_(Walet)/05%3A_Basic_Concepts_of_Theoretical_Particle_Physics/5.01%3A_The_Di%EF%AC%80erence_Between_Relativistic_and_Non-Relativistic_Quantum_MechanicsOne of the key points in particles physics is that special relativity plays a key rôle. As you all know, in ordinary quantum mechanics we ignore relativity. Of course people attempted to generate equa...One of the key points in particles physics is that special relativity plays a key rôle. As you all know, in ordinary quantum mechanics we ignore relativity. Of course people attempted to generate equations for relativistic theories soon after Schrödinger wrote down his equation. There are two such equations, one called the Klein-Gordon and the other one called the Dirac equation.
