4. The Schrdinger Equation for a particle of mass m constrained to move on a circle...

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4. The Schrödinger Equation for a particle of mass "m" constrained to move on a circle of radius "a" is ħ² d'y 21 de - Ey where 0≤0≤2π, I=ma is the moment of inertia, and 0 is the angle that describes the position of the particle around the ring. Show by direct substitution that I (0)= Aene is an eigenfunction of the operator given above and give the eigenvalue (A is a normalization constant). b. Using the boundary condition, y(0)=y(0+2), show that "n" in the wavefunction expression must be an integer. (problem 4, continued) c. Evaluate the normalization constant, A. (the integration element is de). 5. a. Calculate the expectation value for (x²) for a particle in the n = 6 state of the "particle-in-a-box," with box length of a = 3.25 x 10-10 m. b. In class, we found that (x)=a/2, for all energy states of the particle-in-a-box. What is the uncertainty in this value for a particle in the n = 6 state? 4. The Schrödinger Equation for a particle of mass "m" constrained to move on a circle of radius "a" is ħ² d'y 21 de - Ey where 0≤0≤2π, I=ma is the moment of inertia, and 0 is the angle that describes the position of the particle around the ring. Show by direct substitution that I (0)= Aene is an eigenfunction of the operator given above and give the eigenvalue (A is a normalization constant). b. Using the boundary condition, y(0)=y(0+2), show that "n" in the wavefunction expression must be an integer. (problem 4, continued) c. Evaluate the normalization constant, A. (the integration element is de). 5. a. Calculate the expectation value for (x²) for a particle in the n = 6 state of the "particle-in-a-box," with box length of a = 3.25 x 10-10 m. b. In class, we found that (x)=a/2, for all energy states of the particle-in-a-box. What is the uncertainty in this value for a particle in the n = 6 state?

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