Semicircular Potential Well - Analysis

Analysis

Since the wave function is only dependent on the azimuthal angle, the measurable quantities of the system are the angular position and angular momentum, expressed with the operators and respectively.

Using cylindrical coordinates, the operators and are expressed as and respectively, where these observables play a role similar to position and momentum for the particle in a box. The commutation and uncertainty relations for angular position and angular momentum are given as follows:

where and

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