Visualizing the Probability Density Function of a Classical Harmonic Oscillator (Journal Article) (Record no. 45114)
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| fixed length control field | 02328nam a22002057a 4500 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240110132416.0 |
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| 022 ## - INTERNATIONAL STANDARD SERIAL NUMBER | |
| ISSN | 0031-921X |
| 100 ## - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Singh, Mamraj |
| 245 ## - TITLE STATEMENT | |
| Title | Visualizing the Probability Density Function of a Classical Harmonic Oscillator (Journal Article) |
| Remainder of title | |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Washington |
| Name of publisher | :American Association of Physics Teachers |
| Year of publication | , October 2023 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | 588–590p. |
| 440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE | |
| Title | The Physics Teacher |
| Volume number/sequential designation | , Volume 61, Number 7 |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Formatted contents note | ***______{For Hard Copy, Please visit Library.}________***<br/><br/> |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | Abstract: In classical mechanics, the solution of equations of motion of a physical system usually gives well-defined trajectories. With the help of these trajectories, the future progress of the system can be predicted. Therefore, a probability density function (PDF) is not required for such systems and is rarely discussed in classical mechanics. The foundation of quantum mechanics is based on the concept of probability, and it is represented by the square of the wave functions that are solutions to the Schrödinger equation for a given system. In addition, the textbooks refer to the simple harmonic oscillator as an example to compare the quantum and classical probability distribution functions and further explain Bohr's correspondence principle. Therefore, it becomes important to discuss the PDF for a simple harmonic oscillator in a classical framework before introducing the quantum harmonic oscillator to undergraduate students. However, the PDF makes sense in the classical context if any random physical parameter exists in the system or if its position is determined at a random time. The PDF for the classical one-dimensional (1-D) harmonic oscillator is the measure of the time spent by the oscillator in any spatial interval [x, x + dx] about the position x. Theoretical studies on the PDF of a classical harmonic oscillator are readily available in the literature, and they show that the PDF varies from its minimum value to maximum values from the center to the turnaround points. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Harmonic oscillator| Classical mechanics| Probability theory| Educational aids| Correspondence principle |
| 700 ## - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Singh, Amanpal | Kumar, Sandeep |
| 856 ## - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://doi.org/10.1119/5.0094365 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | Periodicals |
| Lost status | Damaged status | Home library | Current library | Date acquired | Koha item type |
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| RIE BPL Library | RIE BPL Library | 10.01.2024 | Periodicals |