Oscillator Representation in Quantum Physics
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Beschreibung
This book describes in detail the oscillator representation method and its application to an approximate solution of the Schrödinger equation with an appropriate interaction Hamiltonian. The method also works well in quantum field theory in the strong coupling regime in calculations of path integrals, as explained by the authors. Furthermore, spectral problems in quantum mechanics are treated.
The book addresses students as well as researchers in quantum physics, quantum field theory, and nuclear and molecular physics.
The investigation ofmost problems of quantum physics leads to the solution of the Schrodinger equation with an appropriate interaction Hamiltonian or potential. However, the exact solutions are known for rather a restricted set of potentials, so that the standard eternal problem that faces us is to find the best effective approximation to the exact solution of the Schrodinger equation under consideration. In the most general form, this problem can be formulated as follows. Let a total Hamiltonian H describing a relativistic (quantum field theory) or a nonrelativistic (quantum mechanics) system be given. Our problem is to solve the Schrodinger equation Hlft = Enlftn, n i. e. , to find the energy spectrum {En} and the proper wave functions {lft } n including the'ground state or vacuum lft = 10). The main idea of any ap o proximation technique is to find a decomposition in such a way that Ha describes our physical system in the "closest to H" manner, and the Schrodinger equation HolJt. (O) = E(O)lJt. (O) n n n can be solved exactly. The interaction Hamiltonian HI is supposed to give small corrections to the zero approximation which can be calculated. In this book, we shall consider the problem of a strong coupling regime in quantum field theory, calculations ofpath or functional integrals over the Gaussian measure and spectral problems in quantum mechanics. Let us con sider these problems briefly.
This book describes in detail the oscillator representation method and its application to an approximate solution of the Schrödinger equation with an appropriate interaction Hamiltonian. It addresses students as well as researchers in quantum physics, quantum field theory, and nuclear and molecular physics.
Autor*in
M. Dineykhan
Themen in »Oscillator Representation in Quantum Physics«
Phase structure canoncial transformation oscillator representation quantum field theory quantum mechanics quantum physics renormalization group