Question

Consider a particle of mass m which can move freely along the x axis from -a/2 to +a/2, but which is strictly prohibited from being found outside this region. The wave function of the particle within the allowed region is ?(x) = A cos(?x / a). (1) What is the energy E in the allowed region? (10 pts) (2) What is the value A? (10 pts)

          Consider a particle of mass m which can move freely along the x axis from -a/2 to +a/2, but which is strictly prohibited from being found outside this region. The wave function of the particle within the allowed region is
?(x) = A cos(?x / a).
(1) What is the energy E in the allowed region? (10 pts)
(2) What is the value A? (10 pts)

Consider a particle of mass m which can move freely along the x axis from -a/2 to +a/2, but which is strictly prohibited from being found outside this region. The wave function of the particle within the allowed region is
?(x) = A cos(?x / a).
(1) What is the energy E in the allowed region? (10 pts)
(2) What is the value A? (10 pts)

Added by Stephanie J.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sparsha S

04/30/2022

Step 1

Given wave function: $\Psi(x) = A\cos(\frac{\pi x}{a})$ The energy operator in one dimension is given by: $\hat{H} = -\frac{\hbar^2}{2m}\frac{d^2}{dx^2}$ The time-independent Schrödinger equation is: $\hat{H}\Psi(x) = E\Psi(x)$ Substitute the wave function into Show more…

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Consider a particle of mass m which can move freely along the x axis from -a/2 to +a/2, but which is strictly prohibited from being found outside this region. The wave function of the particle within the allowed region is ψ(x) = A cos(πx / a). (1) What is the energy E in the allowed region? (10 pts) (2) What is the value A? (10 pts)