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# Creation and annihilation operators

About: Creation and annihilation operators is a research topic. Over the lifetime, 2416 publications have been published within this topic receiving 49871 citations.

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TL;DR: In this article, a method for the calculation of the matrix elements of the logarithm of an operator which gives the exact wavefunction when operating on the wavefunction in the one-electron approximation is proposed.

Abstract: A method is suggested for the calculation of the matrix elements of the logarithm of an operator which gives the exact wavefunction when operating on the wavefunction in the one‐electron approximation. The method is based on the use of the creation and annihilation operators, hole—particle formalism, Wick's theorem, and the technique of Feynman‐like diagrams. The connection of this method with the configuration‐interaction method as well as with the perturbation theory in the quantum‐field theoretical form is discussed. The method is applied to the simple models of nitrogen and benzene molecules. The results are compared with those obtained with the configuration‐interaction method considering all possible configurations within the chosen basis of one‐electron functions.

2,676 citations

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TL;DR: The quantum group SU(2)q is discussed in this paper by a method analogous to that used by Schwinger to develop the quantum theory of angular momentum such theory of the q-analogue of the quantum harmonic oscillator, as is required for this purpose.

Abstract: The quantum group SU(2)q is discussed by a method analogous to that used by Schwinger to develop the quantum theory of angular momentum Such theory of the q-analogue of the quantum harmonic oscillator, as is required for this purpose, is developed

1,555 citations

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Duke University

^{1}TL;DR: In this article, a new realisation of the quantum group SUq(2) is constructed by means of a q-analogue to the Jordan-Schwinger mapping, determining thereby both the complete representation structure and qanalogues to the Wigner and Racah operators.

Abstract: A new realisation of the quantum group SUq(2) is constructed by means of a q-analogue to the Jordan-Schwinger mapping, determining thereby both the complete representation structure and q-analogues to the Wigner and Racah operators. To achieve this realisation, a new elementary object is defined, a q-analogue to the harmonic oscillator. The uncertainty relation for position and momentum in a q-harmonic oscillator is quite unusual.

1,414 citations

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TL;DR: In this paper, a model based on the bilinear products of creation and annihilation operators can be considered as generators of Lie groups and the problem of finding eigenvalues can be greatly simplified by the additional integrals of the motion which are present if the Hamiltonian is constructed so as to commute with invariants of the group.

Abstract: In order to test the validity of various techniques and formalisms developed for treating many-particle systems, a model is constructed which is simple enough to be solved exactly in some cases, but yet is non-trivial. The construction of such models is based on the observation that bilinear products of creation and annihilation operators can be considered as generators of Lie groups. Thus the problem of finding eigenvalues can be greatly simplified by the additional integrals of the motion which are present if the Hamiltonian is constructed so as to commute with invariants of the group. In the present case, the model consists of N fermions distributed in two N-fold degenerate levels and interacting via a monopole-monopole force. It is shown that the model Hamiltonian is easily expressed in terms of quasi-spin operators and exact eigenvalues are obtained. In addition, eigenvalues are calculated with ordinary perturbation theory using values for the number of particles and interaction strength which are appropriate to the more realistic problems of finite nuclei. In subsequent papers we consider the results obtained by various other approximation methods for comparison with the exact results presented here.

1,165 citations

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TL;DR: In this paper, a dual-resonance model of mesons is constructed through the use of creation and annihilation operators having simple anticommutation properties as well as harmonic-oscillator type operators of the conventional model.

Abstract: A new dual-resonance model of mesons is constructed through the use of creation and annihilation operators having simple anticommutation properties as well as harmonic-oscillator type operators of the conventional model. This model has the following virtues not shared by the conventional one: (i) The leading trajectory (ϱ−f0) does not make a particle when it passes through zero. (ii) A π-trajectory lies one-half unit below the ϱ-trajectory. (iii) Trajectories with abnormal-parity couplings to pions, such as ω−A2 and η′, also occur. (iv) The gp, ϱ, f0, ω, A2 and η′ are all forced to have the proper G-parity and isospin. (v) The amplitudes for ππ→ππ and ππ→πω are precisely the ones that have been suggested previously. (vi) The model contains neither embarrassing unobserved low-mass states nor an excessive number of high-mass states. (vii) All the physical states that we have checked have positive norms. To be fair, we should also list some shortcomings of our model: (a) Trajectories with normal-parity couplings occur one-half unit too high. Thus, for example, α ϱ (0) = 1 and α π (0) = 1 2 , so that the π is a tachyon and the ϱ massless. On the other hand, the abnormal-parity trajectories are nicely located. For example, α ω (0) = 1 2 and α η′ (0) = −1 . (b) A straightforward generalization to SU(3) is unsatisfactory because of the non-degeneracy of the ϱ and ω. These features of the model clearly indicate that it is not accurately describing the real world. Perhaps its most important property is that it contains a gauge algebra larger than the Virasoro algebra of the conventional model. We believe that an understanding of this algebra may prove to be very important in the construction of more realistic models.

1,117 citations