Supersymmetric Methods in Quantum, Statistical and Solid State Physics

This is the second edition of Supersymmetric Methods in Quantum, Statistical and Solid State Physics. It provides an accessible introduction to supersymmetric quantum mechanics and its applications in quantum, statistical and solid-state physics, and it now encapsulates the substantial developments made in supersymmetric quantum mechanics in recent years.

Coverage includes classical and quantum versions of Witten's model, and exact spectral properties of the model for the so-called shape invariant potentials. Derivation of the quasi-classical quantisation rule is explored, along with the supersymmetric structure of a classical stochastic dynamical system obeying the Langevin or the Fokker-Planck equation; Pauli's Hamiltonian and its application to the paramagnetism of a non-interacting electron gas in two and three dimensions; and the supersymmetry of Dirac's Hamiltonian, including its application to band structures and graphene. This book captures new developments on exact solutions, such as conditionally exactly solvable systems, coherent states and non-linear algebras, as well as many new interesting aspects within the area of classical field theory, such as stochastic dynamics and the Pauli and Dirac equation. Aimed at graduate students and scientists, this book provides a thorough review of supersymmetric quantum mechanics and now includes problems and solutions.