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JOURNALS || ASIO Journal of Chemistry, Physics, Mathematics & Applied Sciences (ASIO-JCPMAS) [ISSN: 2455-7064 ]
ANALYZING SCHRODINGER EQUATION FOR A PARTICLE IMPINGING ON VERTICAL POTENTIAL STEP BY MATRIX METHOD

Author Names : Rahul Gupta
Page No. : 37-41  Volume 4 Issue 1
Article Overview

ARTICLE DESCRIPTION: 

Rahul Gupta, Rohit Gupta, Dinesh Verma, Analyzing Schrodinger equation for a particle impinging on vertical potential step by matrix method, ASIO Journal of Chemistry, Physics, Mathematics & Applied Sciences (ASIO-JCPMAS), 4(1), 2020: 37-41.

1&2Lecturer of Physics, Department of Applied Sciences, Yogananda College of Engineering and Technology, Jammu, India.

3Professor, Department of Mathematics, NIILM University, Kaithal (Haryana), India.

Doi: 10.2016-28457823;  DOI Link :: http://doi-ds.org/doilink/11.2020-15284517/


Abstract:

Quantum mechanics has been perceived as a requisite ingredient in the curricula of Physics, Chemistry, and Electrical Engineering. By applying Matrix Method, we will analyze the Schrodinger’s equation for a particle impinging on the vertical potential step which is generally done by different algebraic and analytical methods. The matrix method has been applied successfully in science and engineering problems. This paper demonstrates the use of the Matrix Method for analyzing Schrodinger’s equation to find the reflection and transmission coefficients for a particle impinging on the vertical potential step.

Keywords: Matrix Method, Schrodinger Equation, vertical Potential Step.

Reference

[1] N. Zettili, “Quantum Mechanics; Concepts and Applications”.

[2] J. Griffiths, “Introduction to Quantum Mechanics”. Edition 2nd, 2017.

[3] B.N. Srivastava and R.M. Richard, “Quantum Mechanics”. 16th edition, 2017.

[4] H.K. Dass, Advanced Engineering Mathematics, 2014.

[5] 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.

 [6] Rohit Gupta, Rahul Gupta, “Matrix method approach for the temperature distribution and heat flow along a conducting bar connected between two heat sources”, Journal of Emerging Technologies and Innovative Research, Volume 5 Issue 9, September 2018, PP. 210-214.

[7] Rohit Gupta, Rahul Gupta, “Matrix method for deriving the response of a series ?- ?- ? network connected to an excitation voltage source of constant potential”, Pramana Research Journal, Volume 8, Issue 10, 2018.

[8] Rohit Gupta, Rahul Gupta, Sonica Rajput “Response of a parallel ?- ?- ? network connected to an excitation source providing a constant current by matrix method”, International Journal for Research in Engineering Application & Management (IJREAM), Vol-04, Issue-07, Oct 2018.

[9] 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.

[10] P.A.M. Dirac, Principles of quantum mechanics.. Edition: Reprint, 2016