Results 271 to 280 of about 101,189 (313)

Formulation of Quantum Mechanical Perturbation Theory

American Journal of Physics, 1966
A new expression is found for the perturbation energy, with the principle feature that it is in remainder form. The remainder is first applied or manipulated to obtain the familiar infinite series of perturbation theory. Secondly, an iterative procedure for solving the Schrödinger equation is proposed.
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Error bounds for quantum-mechanical perturbation theory

International Journal of Quantum Chemistry, 2009
A new method is described, which yields rigorous upper and lower bounds to the sums over excited states which occur in second-order quantum-mechanical perturbation theory. The only data required are values of certain expectation values over the wave function describing the ground state of the system, and the excitation energy of the first excited state
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Perturbation theory and the classical limit of quantum mechanics

Journal of Mathematical Physics, 1997
We consider the classical limit of quantum mechanics from the viewpoint of perturbation theory. The main focus is time dependent perturbation theory, in particular, the time evolution of a harmonic oscillator coherent state in an anharmonic potential. We explore in detail a perturbation method introduced by Bhaumik and Dutta-Roy [J. Math. Phys.
McRae, S. M., Vrscay, E. R.
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A remark on quantum-mechanical perturbation theory

Mathematical Proceedings of the Cambridge Philosophical Society, 1954
In the course of preparing lectures on elementary quantum theory the author developed a way of presenting time-independent perturbation theory that seems to have some advantages over more familiar presentations. There is nothing fundamentally new in the method, and if any claim of greater power can be made for the new version, it is at best for ...
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Classical and quantum-mechanical observables by perturbation theory

Physics Letters A, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Stationary perturbation theory in the probability representation of quantum mechanics

Journal of Russian Laser Research, 2009
In the probability representation of quantum mechanics, the eigenvalue problems in Hilbert space appear as *-genvalue equations. We show the possibility of employing the nondegenerate stationary perturbation method in the probability representation of quantum mechanics. The perturbed eigentomograms and the eigenvalues of energy are shown to be computed
M. R. Bazrafkan, E. Nahvifard
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On the stationary perturbation theory in quantum mechanics

Soviet Physics Journal, 1980
A simple method is proposed for solving the Shcrodinger equation in the presence of a perturbation. Formally exact expressions are obtained in the form of infinite series for the energies and wave functions without assuming that the perturbation is small.
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Hypervirial theorems and perturbation theory in quantum mechanics

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1965
Previous ideas about the way in which hypervirial theorems might be used to improve approximate wave functions are discussed. To provide a firmer foundation for these ideas, a link is established between hypervirial theorems and perturbation theory. It is proved that if the first-order perturbation correction to the expectation value of an arbitrary ...
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Perturbation Theory for Quantum Mechanics in its Hessenberg-Matrix Representation

International Journal of Modern Physics A, 1997
For years, the partial integrability in quantum mechanics [e.g., the exceptional terminating Lanczos solutions or the so called quasi-exactly solvable "next-to-elementary" systems] represented a challenge in perturbation theory. The main difficulty lied in an incompleteness of the available zero-order wavefunctions and in the related impossibility of ...
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A Note on the Quantum-Mechanical Perturbation Theory

The Journal of Chemical Physics, 1951
The solution of the quantum-mechanical eigenvalue problem is discussed for cases when a series of approximate eigenfunctions is known. If these ``unperturbed'' states are divided into two classes, a perturbation formula is derived giving the influence of one class of states on the other in the final solution.
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