Some Model Hamiltonians in Second Quantized Form

This section is devoted to give an overview on the second quantized forms of various model Hamiltonians used extensively in the everyday practice of quantum chemistry and theoretical solid-state physics. In many scientific publications different quantum chemical models and approximations are introduced or defined by means of the second quantized approach. These models might be as simple as the Hiickel model, for example. Quite often no specific features of second quantization are utilized, but this formalism is used as a convenient language to define various model Hamiltonians. It seems to be useful therefore to review the most frequently applied model Hamiltonians. For further reading we refer to the brief monograph by Del Re et al. (1980). A simple description of the semiempirical schemes discussed below, not using second quantization, can be found in Naray et al. (1987). 

---

Contents Introduction. - Concept of Creation and Annihilation Operators. -Particle Number Operators. - Second Quantized Representation of Quantum Mechanical Operators. - Evaluation of Matrix Elements. - Advantages of Second Quantization. - Illustrative Examples. - Density Matrices. -Connection to Bra and Ket Formalism. - Using Spatial Orbitals. - Some Model Hamiltonians in Second Quantized Form. - The Brillouin Theorem. -Many-Body Perturbation Theory. -Second Quantization for Nonorthogonal Orbitals. - Second Quantization and Hellmann-Feynman Theorem. - Inter-molecular Interactions. - Quasiparticle Transformations. Miscellaneous Topics Related to Second Quantization -Problem Solutions. - References -Index. 

Some Model Hamiltonians in Second Quantized Form... 

---