S C Mishra
Articles written in Pramana – Journal of Physics
Volume 61 Issue 4 October 2003 pp 633-644 Reasearch Articles
Second invariant for two-dimensional classical super systems
S C Mishra Roshan Lal Veena Mishra
Construction of superpotentials for two-dimensional classical super systems (for
Volume 66 Issue 3 March 2006 pp 601-607 Brief Reports
Construction of exact dynamical invariants of two-dimensional classical system
A general method is used for the construction of second constant of motion of fourth order in momenta using the complex coordinates (
Volume 68 Issue 6 June 2007 pp 891-900 Research Articles
Exact solutions to three-dimensional time-dependent Schrödinger equation
With a view to obtain exact analytic solutions to the time-dependent Schrödinger equation for a few potentials of physical interest in three dimensions, transformation-group method is used. Interestingly, the integrals of motion in the new coordinates turn out to be the desired invariants of the systems.
Volume 72 Issue 4 April 2009 pp 647-654 Research Articles
Ram Mehar Singh Fakir Chand S C Mishra
We deal with the difficulties claimed by the author of [
Volume 73 Issue 2 August 2009 pp 349-361
Fakir Chand S C Mishra Ram Mehar Singh
We investigate the quasi-exact solutions of an analogous Schrödinger wave equation for two-dimensional non-Hermitian complex Hamiltonian systems within the framework of an extended complex phase space characterized by $x = x_{1} + ip_{3}$, $y = x_{2} + ip_{4}$, $p_{x} = p_{1} + ix_{3}$, $p_{y} = p_{2} + ix_{4}$. Explicit expressions for the energy eigenvalues and eigenfunctions for ground and first excited states of a two-dimensional $\mathcal{PT}$-symmetric sextic potential and some of its variants are obtained. The eigenvalue spectra are found to be real within some parametric domains.
Volume 75 Issue 4 October 2010 pp 599-605 Research Articles
Eigenvalue spectra of a $\mathcal{PT}$ -symmetric coupled quartic potential in two dimensions
The Schrödinger equation was solved for a generalized $\mathcal{PT}$-symmetric quartic potential in two dimensions. It was found that, under a suitable ansatz for the wave function, the system possessed real and discrete energy eigenvalues. Analytic expressions for the energy eigenvalues and the eigenfunctions for the first four states were obtained. Some constraining relations among the wave function parameters rendered the problem quasi-solvable.
Volume 78 Issue 4 April 2012 pp 513-529 Research Articles
Exact solutions of some physical models using the ($G'/G$)-expansion method
Anand Malik Fakir Chand Hitender Kumar S C Mishra
The ($G'/G$)-expansion method and its simpliﬁed version are used to obtain generalized travelling wave solutions of ﬁve nonlinear evolution equations (NLEEs) of physical importance, viz. the ($2+1$)-dimensional Maccari system, the Pochhammer–Chree equation, the Newell–Whitehead equation, the Fitzhugh–Nagumo equation and the Burger–Fisher equation. A variety of special solutions like periodic, kink–antikink solitons, bell-type solitons etc. can easily be derived from the general results. Three-dimensional proﬁle plots of some of the solutions are also drawn.
Volume 79 Issue 1 July 2012 pp 19-40
Exact complex integrals in two dimensions for shifted harmonic oscillators
Jasvinder Singh Virdi S C Mishra
We use rationalization method to study two-dimensional complex dynamical systems (shifted harmonic oscillator in complex plane) on the extended comples phase space (ECPS). The role and scope of the derived invatiants in the context of various physical problems are high-lighted.
Volume 79 Issue 2 August 2012 pp 173-183
Complex dynamical invariants for two-dimensional complex potentials
J S Virdi F Chand C N Kumar S C Mishra
Complex dynamical invariants are searched out for two-dimensional complex potentials using rationalization method within the framework of an extended complex phase space characterized by $x = x_{1} + ip_{3}. y = x_{2} + ip_{4}, p_{x} = p_{1} + ix_{3}, p_{y} = p_{2} + ix_{4}$. It is found that the cubic oscillator and shifted harmonic oscillator admit quadratic complex invariants. THe obtained invariants may be useful for studying non-Hermitian Hamiltonian systems.
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