Suppose a particle confined to a cavity in a microporous material has a potential energy of the form V(x) = V0 (e-a^2/x^2 - 1). Sketch V(x). What is the value of the force constant corresponding to this potential energy? Would the particle undergo simple harmonic motion? Sketch the likely form of the first two vibrational wavefunctions.

Suppose a particle confined to a cavity in a microporous material has a potential energy of the form V(x) = V0 (e-a^2/x^2 - 1). Sketch V(x). What is the value of the force constant corresponding to this potential energy? Would the particle undergo simple harmonic motion? Sketch the likely form of the first two vibrational wavefunctions.

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Question

Suppose a particle confined to a cavity in a microporous material has a potential energy of the form V(x) = V₀ (e^{-a^2/x^2} - 1). Sketch V(x). What is the value of the force constant corresponding to this potential energy? Would the particle undergo simple harmonic motion? Sketch the likely form of the first two vibrational wavefunctions.

Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.

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