Question 4. Suppose a particle is in an eigenstate of L^2 and Lx with (l, mx) = (1, −1).
(a) What are the possible results of a measurement of Lz and with what probabilities?
(b) Construct the spatial Wave-function corresponding to |l = 1, mx = −1>
Question 4. Suppose a particle is in an eigenstate of L^2 and Lx with (l, mx) = (1, −1).
(a) What are the possible results of a measurement of Lz and with what probabilities?
(b) Construct the spatial Wave-function corresponding to |l = 1, mx = −1>
Question 1. A system is found in the state:
Ψ(r, θ, φ) = A(r) cos(θ) sin(θ) cos(φ)
(a) What are the possible values of a measurement of Lz? What are the associated probabilities?
(b) What is <Lz> in this state?
(c) What is <Lx> in this state?
a freight train moving at an initial speed of 40 m/sec puts on its brakes, producing a deceleration of 0.50 m/sec. a. how long will it take thw train to travel next 100 m ? b. at what speed will it be traveling at the end of this 100 m ?
The eigenvalues and eigenfunctions of a quantum mechanical operator A are denoted
by an and ψn,respectively. If f(x) denotes a function that can be expanded in the
powers of x, show that:
f (A)ψ n = f (an)ψ n
The quantum mechanical wave function for a particle is given by
ψ =
−α
0 , 0
( ) 2 , 0
3
x x
A x e
x
x
.
Determine (i) the normalization constant A and (ii) the most probable position of the
particle.