4. Given these operators A=d/dx and B=x², can you measure the expectation values of the corresponding observables to infinite precision simultaneously?

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.

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

What is the maximum degeneracy of the wavefunctions of a particle confined to the interior of an octahedral hole in a crystal?

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

What is the value of the commutator [P , â4 ].