From the Quantum Mechanical State Space to the Position and Momentum Spaces through a Simple Relation
Abstract
In an attempt to address the need for an alternative presentation of the quantum mechanical position and momentum spaces, we provide a presentation that is more constructive and less calculative than those found in literature. Our approach is based on a simple, intuitively-understood relation that expresses the physical equivalence of the quantum mechanical state space to the position and momentum spaces. With this work, we hope to offer a perspective complementary to those found in standard quantum mechanics textbooks.References
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de la Madrid, R. (2005). The role of the rigged Hilbert space in quantum mechanics. European Journal of Physics, 26 (2), 287-312.
Dirac, P. A. M. (1947). The Principles of Quantum Mechanics, third edition. Clarendon Press.
Gieres, F. (2000). Mathematical surprises and Dirac's formalism in quantum mechanics. Reports on Progress in Physics, 63 (12), 1893.
Griffiths, D. J. (2005). Introduction to Quantum Mechanics, second edition. Pearson Prentice Hall.
Hong, D., Wang, J., & Gardner, R. (2005). Real Analysis with an Introduction to Wavelets and Applications, first edition. Academic Press.
Marshman, E. & Singh, C. (2013). Investigating Student Difficulties with Dirac Notation. Paper presented at the 2013 Physics Education Research Conference.
Retrieved from arXiv:1510.01296.
Marshman, E. & Singh, C. (2015). Student difficulties with quantum states while translating state vectors in Dirac notation to wave functions in position and
momentum representations. Paper presented at the 2015 Physics Education Research Conference. Retrieved from arXiv:1509.04084.
Merzbacher, E. (1998). Quantum Mechanics, third edition. John Wiley & Sons, Inc.
Sakurai, J. J. & Napolitano, J. J. (2011). Modern Quantum Mechanics, second edition. Pearson Education, Inc.
Van Hove, L. (1958). Von Neumann's contributions to quantum theory. Bulletin of the American Mathematical Society, 64 (3), 95-99.
Published
2020-09-16
How to Cite
KONSTANTOGIANNIS, Spiros.
From the Quantum Mechanical State Space to the Position and Momentum Spaces through a Simple Relation.
European Journal of Physics Education, [S.l.], v. 11, n. 2, p. 35-52, sep. 2020.
ISSN 1309-7202.
Available at: <https://eu-journal.org/index.php/EJPE/article/view/265>. Date accessed: 25 apr. 2024.
doi: https://doi.org/10.20308/ejpe.v11i2.265.
Issue
Section
Classroom Physics
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