Classical and Quantum Mechanics of Noncentral Potentials: A by Radhey S. Kaushal

By Radhey S. Kaushal

Non-central forces have a wide selection of functions in classical and quantum mechanics as validated during this ebook. the writer emphasizes the examine of time-dependent potentials, predominantly in dimensions, with no neglecting the fairly good understood time-independent case. the development of invariants within the classical case and the examine of recommendations to Schrödinger's equation, in addition to an in depth presentation of varied mathematical concepts are of major crisis to the writer. The publication addresses theoretical physicists and mathematicians, however it may also be beneficial for electric and mechanical engineers.

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Additional info for Classical and Quantum Mechanics of Noncentral Potentials: A Survey of Two-Dimensional Systems

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Pv 1dxf}- (

38) a.. + a . = - aa .. 40) 1,) ao,i ), I aj ~i IJ = -aao I at. 42i) aao I dX2 - al2 (dV I dXI) - a1 (dV I dXI) a22 (dV + a2 (dV I dX2) = (dao I dt). 37) leads to a Classical Mechanics of Noncentral Time Dependent (TD) Systems 47 larger number of equations here as compared to that of the TID case. Further, a simple analysis of eqs. 1(1)], and subsequently the integration of eqs. 44) + \j/4(1)] X2 + (1/2)\j/2(1) Xf +(1 I 2) 'lf 5 (t) x 1 + (1 I 2) 'JI 6 (t). Xi Here '1'/S are the arbitrary functions of t.

While the construction of the second invariant is fmally carried out in a polynomial (in momenta) form, several other of its forms are also discussed. As a matter of fact the existence of a polynomial form is desirable from the physics point of view; however, the occurence of any other functional form of the invariant can also simplify the solution of the problem. While only passing remarks are made for the Painleve and Lax-pair methods with reference to the construction of the second invariant, the rationalization method on the lines of Whittaker, on the other hand, is discussed in great detail.

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