Answered: The expectation value of a function… | bartleby

Related questions

Question

The expectation value of a function f(x), denoted by (f(x)), is given by
(f(x)) = f(x)\(x)|³dx
+00
Yn(x) =
where (x) is the normalised wave function.
A one-dimensional box is on the x-axis in the region of 0 ≤ x ≤ L. The normalised wave
functions for a particle in the box are given by
-sin
-8
Calculate (x) and (x²) for a particle in the nth state.
n = 1, 2, 3, ....

Expert Solution

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

The wave function W(x,t)=Ax^4 where A is a constant. If the particle in the box W is normalized. W(x)=Ax^4 (A x squared), for 0<=x<=1, and W(x) = 0 anywhere. A is a constant. Calculate the probability of getting a particle for the range x1 = 0 to x2 = 1/3 a. 1 × 10^-5 b. 2 × 10^-5 c. 3 × 10^-5 d. 4 × 10^-5
= = An electron having total energy E 4.60 eV approaches a rectangular energy barrier with U■5.10 eV and L-950 pm as shown in the figure below. Classically, the electron cannot pass through the barrier because E < U. Quantum-mechanically, however, the probability of tunneling is not zero. Energy E U 0 i (a) Calculate this probability, which is the transmission coefficient. (Use 9.11 x 10-31 kg for the mass of an electron, 1.055 x 10-34] s for h, and note that there are 1.60 x 10-19 J per eV.) (b) To what value would the width L of the potential barrier have to be increased for the chance of an incident 4.60-eV electron tunneling through the barrier to be one in one million? nm
The wave function of a particle at time t= 0 is given by w(0) = (4,) +|u2})), where |u,) and u,) the normalized eigenstates with eigenvalues E and E, are respectively, (E, > E, ). The shortest time after which y(t) will become orthogonal to |w(0)) is - ħn (а) 2(E, – E,) (b) E, - E, (c) E, - E, (d) E, - E,