Consider a 1D problem for a particle of mass m that is free to move in...

 

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Consider a 1D problem for a particle of mass m that is free to move in the interval z € [0, a]. The potential V(x) is zero in this interval and infinite elsewhere. For that system consider a solution of the Schrödinger equation of the form NT = N sin (re-ion(t) T = [0, a], a 1 and ₁(x, t) = 0 for x < 0 and > a. Here n ≥ 1 is an integer. (a) Find the expression for the (real) phase (t) so that the above wavefunction solves the Schrödinger equation. Find the normalization constant N. (b) Use V, (1, 0) to calculate (r), (x²), and Ar. n (c) Use V,(,0) to calculate (p), (p²), and Ap. (d) Is the uncertainty inequality satisfied? Is it saturated? (e) What answers in (b) and (c) change for V₁(x, t)? Explain. Consider a 1D problem for a particle of mass m that is free to move in the interval z € [0, a]. The potential V(x) is zero in this interval and infinite elsewhere. For that system consider a solution of the Schrödinger equation of the form NT = N sin (re-ion(t) T = [0, a], a 1 and ₁(x, t) = 0 for x < 0 and > a. Here n ≥ 1 is an integer. (a) Find the expression for the (real) phase (t) so that the above wavefunction solves the Schrödinger equation. Find the normalization constant N. (b) Use V, (1, 0) to calculate (r), (x²), and Ar. n (c) Use V,(,0) to calculate (p), (p²), and Ap. (d) Is the uncertainty inequality satisfied? Is it saturated? (e) What answers in (b) and (c) change for V₁(x, t)? Explain.

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A0 Schrodinger equation D 2a 0 Particle in an infinite potential ay 1h 28 21 22 VR P in t Vx 0 ibit ... View the full answer