arXiv subjects

Saravanan Rajendran

Publications and source records attributed to Saravanan Rajendran.

3 recordsLinked to original sources

arXiv2020

Diffusion-reaction approach to electronic relaxation in solution: Exact time domain solution for Dirac delta function sink model

We propose an analytical method for finding the time domain solution for the problem of electronic relaxation of a molecule in solution. The relaxation process is modeled by the decay of a diffusing probability distribution through an absorbing sink. In our model, the diffusive motion is modeled using the Smoluchowski equation for harmonic potential and the sink is represented by a Dirac Delta function of arbitrary strength and position. This has been an unsolved problem for a long time and is of immense importance as a model for understanding non-radiative electronic relaxation of a molecule in solution. Our solution can be used to understand various reaction-diffusion problems.

physics.chem-ph↗

arXiv2020

An exact analytical scheme using a new potential to solve one-dimensional quantum systems

We propose an exact method for solving a one-dimensional Schrödinger equation. An arbitrary potential is represented by the collection of short-width potentials. For building the collection scheme, a new solvable potential is introduced. It is based on the simple expansion of the wavefunction of the introduced potential. The illustration of the scheme is done by reproducing the results of the rectangular potential. The scheme has computational advantages and the transmission properties, eigenenergies can be calculated efficiently. The presented scheme is compared with the other similar schemes in terms of computational complexity, analytical solubility, etc.. A \textit{Mathematica} code is provided in the supplementary file that solves the Schrödinger equation with arbitrary potential function $V(x)$ and effective mass $m(x)$.

quant-ph↗

arXiv2018

Exact dynamics of a Gaussian wave-packet in two potential curves coupled at a point

We present a method to calculate exact dynamics of a wave-packet in a quantum two-state problem with Dirac delta coupling. The advantage of our method is that the calculations are done in the time domain. Hence inverting the solutions from other domains (Laplace or Fourier domain) do not intervene us from presenting the solution in the time domain. The initial wave packet is considered to be a Gaussian function. The wave propagation in the quantum state is governed by time-dependent Schrödinger equation and the coupling is given by non-diagonal element in the matrix representation. We present the exact analytic forms of the wave function for both the states in the time domain.

quant-ph↗