(Solution) - For each of the following systems give the expression for -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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For each of the following systems, give the expression for dt and give the limits of each variable in the equation ?|?|2 d? = 1.
(a) The particle in a one-dimensional box of length l.
(b) The one-dimensional harmonic oscillator.
(c) A one-particle, three-dimensional system where Cartesian coordinates are used.
(d) Internal motion in the hydrogen atom, using spherical coordinates.