Expectation of Momentum in a Classical (Infinite) Potential Well

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Homework Help Overview

The discussion revolves around calculating the expectation of momentum for a classical particle in an infinite potential well. The original poster introduces the wavefunction and attempts to derive the expectation value of momentum, referencing quantum mechanics for comparison.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the implications of using a classical versus quantum approach to the problem, questioning the necessity of boundary conditions and the form of the wavefunction. There are discussions about the nature of the wavefunction and its behavior at the boundaries of the well.

Discussion Status

Participants are actively questioning assumptions about the wavefunction and its normalization. Some suggest that the wavefunction must vanish at the boundaries, while others express uncertainty about how to reconcile classical and quantum descriptions. There is a recognition of the complexities involved in treating a classical particle with wave-like properties.

Contextual Notes

There are ongoing discussions about the definitions and implications of a "classical particle" in the context of wave mechanics, as well as the challenges posed by the requirement for uniform velocity in the wave description.

  • #31
To elaborate on @jtbell #24. The expectation value, as you know, is an average.

Suppose you performed ##N## measurements of the momentum at random intervals and you got ##N_1## values at ##+p## and ##N_2## at ##-p##, where ##N=N_1+N_2##. What is the average value of the momentum?

Suppose you flip a fair coin ##N## times and you get ##N_1## tails and ##N_2## heads. You assign +1 point to tails and -1 point to heads. How would you express the average of the flips as a number? What do you think the a priori average could be before you do any measurements?
 

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