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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1491-1497 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A sufficient condition to relate the general solutions of two different bidimensional problems, both in classical and quantum mechanics, is found. The point transformation, as well as the explicit construction of the related potentials, is presented. The procedure is then used in geometrical optics, the vibrating membrane, and other physical systems in two dimensions. Several examples and applications are worked out.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 142-146 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This work starts with classical equations of motion and sets very general quantization conditions (commutation relations). It is proved that these conditions imply that the equations of motion are equivalent to the Euler–Lagrange equations of a Lagrangian L. The result is a generalization of work by Feynman, recently reported by Dyson [Am. J. Phys. 58, 209–211 (1990)]. The Lagrangian L need not be unique. Examples are given, including classical equations that do not come from a Lagrangian and therefore cannot be quantized consistently.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 234-238 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Sufficient conditions on the Christoffel symbols and metric tensors to insure the existence of affine collineations in Riemann spaces are obtained. A proof of the group property of affine collineations is given. Several examples of physically relevant Riemannian spaces admitting affine collineations are presented and the constants of motion are constructed.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 2968-2974 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new (non-Noetherian) symmetry transformation for the small oscillations problem is exhibited. A novel way to solve this classical problem, based on conservation laws constructed using the new symmetry, is presented. Applications of these results to other fields of physics are outlined.
    Type of Medium: Electronic Resource
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