Kamal Bhattacharyya

Quantum decay and the Mandelstam-Tamm-energy inequality

The Mandelstam-Tamm time-energy inequality is exploited to obtain a transparent expression of the lifetime-energy uncertainty relation for decaying quantum systems along with some useful features of the quantum non-decay probability.

On the nonlinear manifold energy variation method and excited state calculations

Abstract A coupled linear-nonlinear variational scheme is adopted to highlight the efficacy of the method of minimisation of manifold energy in relation to the conventional method. Particularly, the viability of this route in computing excited state energies is assessed. An unconstrained minimisation technique for excited states, with even better performance, is also put forward in the same context. Demonstrative calculations on various anharmonic oscillators reveal a substantial computational gain in every case.

Comment on `Quantum-mechanical Carnot engine'

The equations governing adiabatic and isothermal quantum processes involved in an ideal two-state quantum heat engine are modified when the ideality restriction is removed. We seek and study a few situations to determine the nature and magnitude of the modifications. If one confines such systems well within the classical turning point, we show how one can profitably employ the Wilson-Sommerfeld quantization rule to estimate the leading correction terms due to non-ideality. The endeavour is likely to be important in studies on practical quantum engines.

On the temperature dependence of the partition function: Molecular free internal rotation

Abstract A systematic approximation scheme for studying the partition function at intermediate temperature range has been presented, referring especially to molecular free internal rotation as a test case, and compared thoroughly with quite a few other approximants in vogue. The relative merits of the strategies are also analysed.

On the Padé method for sequence acceleration and calculation of Madelung constants

Abstract An iterative variant of Pade approximants (PA) is presented and employed to accelerate convergence of sequences. Pilot calculations on partial lattice sums for NaCl and CsCl crystals have been explicitly shown to offer accurate estimates of their Madelung constants.

Some applications of the particle-in-a-box eigenfunctions: Fast-convergent variational and related calculations

Abstract Eigenfunctions of the quantum mechanical particle-in-a-box problem are shown to lead to a new trigonometric expansion scheme with good convergence properties. This hitherto unexpansion strategy is found to be quite efficient in variational calculations and as an alternative to the Fourier series. Demonstrative computations involve a few one-dimensional models of confining potentials for bound states and pulses of various shapes in signal analysis.

Single-substrate enzyme kinetics: the quasi-steady-state approximation and beyond

We analyze the standard model of enzyme-catalyzed reactions at various substrate-enzyme ratios by adopting a different scaling scheme and computational procedure. The regions of validity of the quasi-steady-state approximation are noted. Certain prevalent conditions are checked and compared against the actual findings. Efficacies of a few other measures, obtained from the present work, are highlighted. Some recent observations are rationalized, particularly at moderate and high enzyme concentrations.

Perturbative and nonperturbative studies with the delta function potential

We show that the δ-function potential can be exploited along with perturbation theory to yield the result of certain infinite series. The idea is that any exactly soluble potential, if coupled with a δ function potential, remains exactly soluble. We use the strength of the δ function as an expansion parameter and express the second-order energy shift as an infinite sum in perturbation theory. The analytical solution is used to determine the second-order energy shift and hence the sum of an infinite series. By an appropriate choice of the unperturbed system, we can show the importance of the continuum in the energy shift of bound states.

Forcing of convergence in pathological self-consistent-field calculations: a Padé-(MC)SCF strategy

The efficacy of a Pade-(MC)SCF strategy both in accelerating slowly convergent iterative sequences and forcing convergence in pathologically divergent problems is explored. Comparison is made with the traditional level- (root-)shifted (MC)SCF approach. Finally, the performance of a coupled Pade-level-shifted (MC)SCF scheme in cases of intrinsic divergence is presented.

Notes on polynomial perturbation problems

Abstract The convergence behaviour of Rayleigh-Schrodinger perturbation theory for polynomial perturbation problems is discussed with some specific examples. It is emphasized that the choice of the perturbation parameter becomes crucial in this issue, in the light of certain seemingly contradictory conclusions drawn recently.