By M. Dineykhan, G.V. Efimov, G. Ganbold, S.N. Nedelko

This ebook describes intimately the oscillator illustration process and its program to an approximate answer of the Schr?dinger equation with a suitable interplay Hamiltonian. the tactic additionally works good in quantum box conception within the robust coupling regime in calculations of course integrals, as defined by way of the authors. moreover, spectral difficulties in quantum mechanics are taken care of.

The booklet addresses scholars in addition to researchers in quantum physics, quantum box thought, and nuclear and molecular physics.

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**Extra info for Oscillator Representation in Quantum Physics**

**Example text**

Hence 10; e} is the vacuum with respect to operators a, ,8 and the corresponding Fock space 1i[a,,8] can be constructed. This consideration illustrates that the spaces 1i[a, b] and 1i[a,,8] correspond to two unitary nonequivalent CR representations in the sense that there is a vector in 1i[a,,8] which can not be represented as a superposition of the basis vectors of the space 1i[a, b]. Moreover, this statement is true for any vector of the space H[a, ,8]. One can say that the spaces 1i[a, b] and 1i[a,,8] are orthogonal to each other.

Here Ho is the standard free Hamiltonian. An interaction Hamiltonian HI contains the field operators in degree more then two. The operator Hct is determined by H o and HI and corresponds to the equivalent R-schemes in all representations. 1. ) = M(v) = C. 1. 33) is realized by using of the compensating RG transformation. 3. As a result we get a set of nonequivalent CR representations describing different phases of the system under consideration. The main physical characteristic of the ground state of any system is the free energy density F, which is related to the vacuum energy density E as follows: F = E-TS, where S is the entropy density.

Moreover, this statement is true for any vector of the space H[a, ,8]. One can say that the spaces 1i[a, b] and 1i[a,,8] are orthogonal to each other. At the same time, the above consideration does not mean that it is impossible to define the action of the operators a and ,8 on the vectors of 1i[a, b]. 22). 22) can not be realized as a unitary transformation and the operators a and ,8 are not annihilation operators on the space 1i[a, b], where there is no vacuum related to a and ,8. Let us consider another canonical transformation generating nonequivalent representations.