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This textbook provides a comprehensive treatment of quantum mechanics from a mathematics perspective. In addition to traditional topics, it gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics.

The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrodinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.