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JOURNALS || ASIO Journal of Chemistry, Physics, Mathematics & Applied Sciences (ASIO-JCPMAS) [ISSN: 2455-7064 ]
SOLVING SCHRODINGER EQUATION FOR A QUANTUM MECHANICAL PARTICLE BY A NEW INTEGRAL TRANSFORM: ROHIT TRANSFORM

Author Names : Rohit Gupta
Page No. : 32-36  Volume 4 Issue 1
Article Overview

ARTICLE DESCRIPTION: 

Rohit Gupta, Rahul Gupta, Dinesh Verma, Solving Schrodinger equation for a quantum mechanical particle by a new integral transform: Rohit transform, ASIO Journal of Chemistry, Physics, Mathematics & Applied Sciences (ASIO-JCPMAS), 2020, 4(1): 32-36. 

Lecturer of Physics, Department of Applied Sciences, Yogananda College of Engineering and Technology, Jammu, India.

Lecturer of Physics, Department of Applied Sciences, Yogananda College of Engineering and Technology, Jammu, India.

Professor, Department of Mathematics, NIILM University, Kaithal (Haryana), India.

Doi: 10.2016-28457823;  DOI Link :: http://doi-ds.org/doilink/10.2020-36786965/


Abstract:

Quantum mechanics explains the nature of atomic particles at the small scale of energy and most of the boundary value problems in this mechanics are generally solved by ordinary algebraic or analytical methods or calculus approach or by Fourier Transform. In this paper, a new approach is presented to solve the one-dimensional time-independent Schrodinger’s equation for a particle inside the one-dimensional infinitely high potential box and for a particle impinging on the vertical potential step by applying a new integral transform called Rohit Transform (RT) and demonstrated it to find the eigen values and eigen functions for a particle inside the one-dimensional infinitely high potential box and for a particle impinging on the vertical potential step to find the reflection and transmission coefficients.

Keywords: Rohit Transform (RT), Schrodinger Equation, Vertical Potential Step, and Infinitely high Potential Box.

Reference

[1] Introduction to Quantum mechanics by David j. Griffiths. Publisher: Cambridge University Press. 2nd edition.

[2] Quantum mechanics by B.N. Srivastava, R.M. Richaria. Publisher: Pragati Prakashan Meerut. 16th edition.

[3] Principles of quantum mechanics by P.A.M. Dirac. Publisher: Oxford University Press. Edition: Reprint, 2016.

[4] Nouredine Zettili, Quantum Mechanics: Concepts and Applications. Publisher: John Wiley and Sons. 2nd edition.

[5] Rohit Gupta, “On novel integral transform: Rohit Transform and its application to boundary value problems”, ASIO Journal of Chemistry, Physics, Mathematics and Applied Sciences (ASIO-JCPMAS), Volume 4, Issue 1, 2020, PP. 08-13.

[6] Rohit Gupta, Rahul Gupta, Dinesh Verma, Eigen Energy Values and Eigen Functions of a Particle in an Infinite Square Well Potential by Laplace Transforms, International Journal of Innovative Technology and Exploring Engineering, Volume 8 Issue 3, January 2019, PP 6-9.

 [7] Rohit Gupta, Rahul Gupta, Matrix Method For Solving The Schrodinger’s Time - Independent Equation To Obtain The Eigen Functions And Eigen Energy Values of A Particle Inside The Infinite Square Well Potential, IOSR Journal of Applied Physics (IOSR-JAP), Volume 10, Issue 5 Ver. I (Sep. – Oct. 2018), PP 01-05.

 [8] Rohit Gupta, Tarun Singhal, Dinesh Verma, Quantum mechanical reflection and transmission coefficients for a particle through a one-dimensional vertical step potential, International Journal of Innovative Technology and Exploring Engineering, Volume-8 Issue-11, September 2019, PP 2882-2886.

[9] Rohit Gupta, Rahul Gupta, Dr. Dinesh Verma, Eigenenergy values and Eigenfunctions of one dimensional quantum mechanical harmonic oscillator, IOSR Journal of Engineering (IOSRJEN), Vol. 09, Issue 1 (January. 2019),V (III), PP 17-21.