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V Balakrishnan
Articles written in Resonance – Journal of Science Education
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Volume 1 Issue 1 January 1996 pp 110-114 Book Review
A Joyous Romp Through Basic Physics
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Volume 1 Issue 8 August 1996 pp 8-15 Series Article
What can the Answe be? - Elementary Vector Analysis
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Volume 1 Issue 10 October 1996 pp 6-13 Series Article
What Can the Answer be? Reciprocal Basis and Dual Vectors
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Volume 2 Issue 5 May 1997 pp 8-14 Series Article
What Can the Answer be? Reciprocal Basis in Two Dimensions and Other Nice Things
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Volume 2 Issue 7 July 1997 pp 20-26 Series Article
What Can the Answer be? Reciprocal Basis in n-Dimensions and other Ramifications
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Volume 3 Issue 2 February 1998 pp 83-85 Book Review
Dreams of a Final Theory – The Search for the Fundamental Laws of Nature
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Volume 4 Issue 4 April 1999 pp 93-95 Book Review
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Volume 4 Issue 10 October 1999 pp 61-68 Classroom
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Volume 6 Issue 1 January 2001 pp 18-27 General Article
Iterated Functions and Intermittency
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Volume 8 Issue 8 August 2003 pp 48-58 General Article
All about the Dirac Delta Function (?)
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Volume 9 Issue 6 June 2004 pp 30-38 General Article
Wave Propagation: Odd is Better, but Three is Best - The Formal Solution of the Wave Equation
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Volume 9 Issue 7 July 2004 pp 8-17 General Article
Wave Propagation: Odd is Better, but Three is Best - Propagation in Spaces of Different Dimensions
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Volume 10 Issue 3 March 2005 pp 35-56 General Article
Vasant Natarajan V Balakrishnan N Mukunda
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Volume 10 Issue 12 December 2005 pp 12-19
What can the Answer be? - Elementary Vector Analysis
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Volume 13 Issue 9 September 2008 pp 843-865 General Article
Space and Time in Life and Science
Vasant Natarajan V Balakrishnan N Mukunda
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Volume 16 Issue 2 February 2011 pp 129-151 General Article
Symmetries and Conservation Laws in Classical and Quantum Mechanics - Classical Mechanics
K S Mallesh S Chaturvedi V Balakrishnan R Simon N Mukunda
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Volume 16 Issue 3 March 2011 pp 254-273 General Article
Symmetries and Conservation Laws in Classical and Quantum Mechanics - Quantum Mechanics
K S Mallesh S Chaturvedi V Balakrishnan R Simon N Mukunda
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Volume 16 Issue 9 September 2011 pp 886-889 Book Review
A Joyous Romp Through Basic Physics - The Work of a Magician of the Highest Calibre
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Volume 17 Issue 1 January 2012 pp 23-32 General Article
Ehrenfest's Theorem and Nonclassical States of Light - Ehrenfest's Theorem in Quantum Mechanics
Lijo T George C Sudheesh S Lakshmibala V Balakrishnan
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Volume 17 Issue 2 February 2012 pp 192-211 General Article
Ehrenfest's Theorem and Nonclassical States of Light - Dynamics of Nonclassical States of Light
Lijo T George C Sudheesh S Lakshmibala V Balakrishnan
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Volume 27 Issue 7 July 2022 pp 1135-1153 General Article
Particle in a Box: A Basic Paradigm in Quantum Mechanics - Part 1
The problem of a particle moving freely inside a box with rigid, perfectly reflecting walls is a standard exercise in basic quantum mechanics (QM), the box being taken to be a line interval, a square, and a cube, respectively, in the 1, 2, and 3 dimensional cases. The problem illustrates several aspects of QM, such as stationary states, uncertainty relations, eigen-values, eigenfunctions, orthonormality, completeness, and so on. The purpose of this two-part article is to provide some insights into how the particle-in-a-box problem acts as a paradigm for the understanding of these and other aspects, such as the roles played by dimensionality, discrete and continuous symmetry, degeneracy, etc. Further, we shall also see (in Part 2) how the same problem leads directly to some non-trivial matters such as quantum chaos and deep results in mathematical physics. Finally, it must be emphasized that the particle-in-a-box problem is no longer just a theoretical exercise. With modern technology, it is physically realized in different kinds of nanostructures such as nanowires, atomic corrals, quantum dots, conjugated polymers, among others. This makes it all the more important to analyze various problems of this class and their solutions.
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Volume 27 Issue 8 August 2022 pp 1327-1340 General Article
Particle in a Box: A Basic Paradigm in Quantum Mechanics - Part 2
The problem of a particle moving freely inside a region with rigid, perfectly reflecting walls serves as a paradigm to illustrate numerous aspects of quantum mechanics (QM). In Part 11 of this two-part article, we discussed several of these aspects using, respectively, a line segment, a ring, and a square as the region concerned. In the present part, we shall consider the cases of a circular region and a surface of constant positive curvature (a sphere). We shall then comment on the general case of a dynamical billiard. Finally, we turn to the inverse problem: given the energy spectrum of a particle moving freely inside a region, what can be deduced about the geometrical properties of the region? Some important results in this regard will be described in brief.
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Resonance – Journal of Science Education
Current Issue
Volume 28 | Issue 9
September 2023
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Resonance – Journal of Science Education | News
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Posted on 13 July 2021 -
Workshop in Algebra, 7–9 September 2021
Posted on 9 August 2021
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