• S S Vasan

      Articles written in Pramana – Journal of Physics

    • Exact energy eigenvalues by summation of thejwkb series

      M Seetharaman S S Vasan S Ravichandran

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      For the potentialV(x)=V0 tan2x, the corrections to the lowest orderjwkb (Bohr-Sommerfeld) energy quantization rule are non-zero. These higher order corrections are explicitly computed using the formalism of Dunham. The resultingjwkb series for the energy eigenvalues is summable, and yields the exact bound state spectrum.

    • Stability of theS matrix pole

      G Rajasekaran S S Vasan

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      We show how the position and residue of theS matrix pole can remain stable under changes in the form of the parametrization of theS matrix elements. We also derive a relation among the shifts in the Breit-Wigner resonance parameters under the same changes and verify the relation numerically for the case of Δ(1232). Despite its stability, the pole does not provide a unique definition of the resonance because of the existence of shadow poles.

    • Relation between Green’s functions for different potentials

      S S Vasan M Seetharaman K Raghunathan

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      A general relation between the energy-dependent Green’s functions for different potentials is derived in a simple and direct manner. This interesting connection enables the eigenstates of one physical system to be deduced from those of a related system. The derivation is based on the Schrödinger equation and provides an independent justification for the technique of path-dependent time transformation used in path integration.

    • On the solution of an anisotropic nonquadratic potential

      S S Vasan M Seetharaman K Raghunathan

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      The Schrodinger-Green function is constructed for an anisotropic non-quadratic potential which has been studied in recent literature. The eigen energies and wavefunctions are readily obtained. Our analysis shows that the wavefunctions given in earlier literature are incorrect and the source of the error is pointed out. A semiclassical treatment of the problem is also presented in support of some of our observations.

    • A JWKB analysis of the sextic anharmonic oscillator in d dimensions

      S S Vasan M Seetharaman L Sushama

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      On the basis of a radial generalization of the JWKB quantization rule, which incorporates higher orders of the approximation, an explicit analytical formula is derived for the energy levels of the three-dimensional sextic anharmonic oscillator. The formula exhibits the scaling property of the exact eigenvalues, and is readily generalized to any dimension. The predicted results are in good agreement with known numerical values.

    • A new perturbative approach to the classical anharmonic oscillator

      S S Vasan M Seetharaman

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      The periodic motion of the classical anharmonic oscillator characterized by the potentialV(x)=1/2x2+λ/2k x2k is considered. The period is first determined to all orders inλ in a perturbative series. Making use of this, the solution of the nonlinear equation of motion is then expressed in the form of a Fourier series. The Fourier coefficients are obtained by solving simple algebraic relations. Secular terms are inherently absent in this perturbative scheme. Explicit solution is presented for generalk up to the second order, from which the Duffing and the sextic oscillator results follow as special cases.

    • The Coulomb Green’s function revisited

      S S Vasan M Seetharaman

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      It is demonstrated how the energy-dependent Green’s function for the Schrödinger-Coulomb problem can be deduced from a knowledge of the harmonic oscillator time-propagator. All the known results of the Coulomb system are shown to be elegantly derivable from such a connection.

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