Question

The wave functions for a particle restricted to lie in a rectangular region of length "p" and "q" (a particle in a two-dimensional box) are: ?_nx,ny(x,y) = (4/pq)^1/2 sin(nx?x/p) sin(ny?y/q) Where, 0 ? x ? p and 0 ? x ? q. Show that these wave functions are normalized.

          The wave functions for a particle restricted to lie in a rectangular region of length "p" and "q" (a particle in a two-dimensional box) are:

?_nx,ny(x,y) = (4/pq)^1/2 sin(nx?x/p) sin(ny?y/q)

Where, 0 ? x ? p and 0 ? x ? q. Show that these wave functions are normalized.

The wave functions for a particle restricted to lie in a rectangular region of length "p" and "q" (a particle in a two-dimensional box) are:

?nx,ny(x,y) = (4/pq)^1/2 sin(nx?x/p) sin(ny?y/q)

Where, 0 ? x ? p and 0 ? x ? q. Show that these wave functions are normalized.

Added by Lourdes W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Shaiju T

04/20/2022

Step 1

Step 1: Write down the given wave function for the particle in a two-dimensional box: \[ \Psi_{n_x, n_y}(x, y) = \left(\frac{4}{pq}\right)^{1/2} \sin\left(\frac{n_x \pi x}{p}\right) \sin\left(\frac{n_y \pi y}{q}\right) \] Show more…

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The wave functions for a particle restricted to lie in a rectangular region of length "p" and "q" (a particle in a two-dimensional box) are: Έ_nx,ny(x,y) = (4/pq)^1/2 sin(nxΑx/p) sin(nyΑy/q) Where, 0 ≤ x ≤ p and 0 ≤ y ≤ q. Show that these wave functions are normalized.