Which of these choices is the expectation value of momentum squared p2 for a particle in the state n = 1 in a square well potential. hL/2 h/4L^2 h^2/L^2 h^2/4L^2 0

4) Is the function = B sin (bx) an eigenfunction of the operator d/dx = = d/dx if B and b are constants and real numbers? Show your work in detail.

Consider a single particle with rest mass m residing in a one-dimensional space, x. This particle experiences a potential energy V(x) = ∞ for x a, and a potential energy V(x) = 0 for 0 < x < a. The solutions to the Schrödinger Equation for this system are 12. 2 Vn(x) : sin a where n is the state's quantum number. Show that the ground state wave function is normalized.

What is the lowest possible value of the angular momentum quantum number (l) when the magnetic quantum number (ml) is −1?

Confirm that the wavefunction Y(x,t)= e(px-Et )/h is a solution of the one-dimensional time- 2. dependent Schrödinger equation?

A particle rotating on the surface of a sphere with fixed r has the quantum numbers I = 3 and mj = 1. What is the magnitude of the angular momentum? V12 h O 12n? O 12h

please answer #2

1:51 PM Sun Oct 9 -1/2 5) For a particle on a ring with the wavefunction: () = π kinetic energy of the particle using the operator K = -1/2 Y(0) = IT 21T K=-ħ²d² 21d² 2 cos ($) = kdo T (17¹/2)² 211 - f = "Cos (0) . # de TỈ Cos (O). t d. TỈ Cosco) do = 21 0 21 cos() calculate the average cos(0). -ħ² d² do 21 do² 10:52 @ 79% + : 5 9 +