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Oscillator Representation in Quantum Physics (Paperback, Softcover reprint of the original 1st ed. 1995)
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Oscillator Representation in Quantum Physics (Paperback, Softcover reprint of the original 1st ed. 1995)
Series: Lecture Notes in Physics Monographs, 26
Expected to ship within 10 - 15 working days
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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."
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