000			02328nam a22002057a 4500
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008			240109b ||||| |||| 00| 0 eng d
022			_a0031-921X
100			_aSingh, Mamraj
245			_aVisualizing the Probability Density Function of a Classical Harmonic Oscillator (Journal Article) _b
260			_aWashington _b:American Association of Physics Teachers _c, October 2023
300			_a588–590p.
440			_aThe Physics Teacher _v, Volume 61, Number 7
505			_a***______{For Hard Copy, Please visit Library.}________***
520			_aAbstract: 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			_aHarmonic oscillator| Classical mechanics| Probability theory| Educational aids| Correspondence principle
700			_aSingh, Amanpal | Kumar, Sandeep
856			_uhttps://doi.org/10.1119/5.0094365
942			_cPER
999			_c45114 _d45113