Psi(x) = {Ax(a-x), for 0 lessthanorequalto X lessthanorequalto A otherwise Psi(x) to compute value of A...
-ax²12 directly into the Schroedinger equation, as broken down in the following steps. Show that the energy of a simple harmonic oscillator in the n = 0 state is 1ho/2 by substituting the wave function wo = Ae First, calculate dvo/dx, using A, x, and a. dyo/dx = Second, calculate dvo/dx?, using A, x, and a. dyo/dx2 = Third, calculate a?x?wo-dayo/dx?, using A, x, and a. a3x240 - dạyo/dx? Fourth, calculate (a?x240-d2vo/dx2)/yo, using A, X, and a. (22x200-2vo/dx?)/- 1 Finally,...
Find parts a and b.
Consider the three-dimensional cubic well V = {(0 if
0<x<a, 0<y<a, 0<z<a), (infinity otherwise).
The stationary states are psi^(0) (x, Y, z) =
(2/a)^(3/2)sin(npix/a)sin(npiy/a) sin(npiz/a), where nx, ny , and
nz are integers.
The corresponding allowed energies are E^0 =
(((pi^2)(hbar^2))/2m(a^2))(nx^2+ny^2+nz^2).
Now let us introduce perturbation V={(V0 if
0<x<(a/2), 0<y<(a/2)), (0 otherwise)
a) Find the first-order correction to the ground state
energy.
b) Find the first-order correction to the first
excited state.
1. Consider the...
please use the given psi(0) and psi(1) and go through the full
working please
(a) Show by direct integration that both yo and yi are normalised. (b) By direct integration, calculate the expectation value of x in each of these two states: (c) Calculate the expectation value of momentum in each of these two states: (d) Show that both momentum and position are not well-defined in these two states i.e., wo and yi are not eigenfunctions of either the position...
Question blow and I need a, b and c, please help me.
(a) Evaluate an expression for the expectation value of the potential energy for the n 3, 1-1, m = 1 wavefunction of the hydrogen atom. You need to compute the integral, where e2 [4 marks] 0 wave- 6 marks] [2 marks] Write the answer in terms of h. e and me (b) Calculate the expectation value of the kinetic energy for the n-1,- function of the hydrogen atom....
Calculate the expectation value <r> of an electron in the state of n=1 and 1-0 of the hydrogen atom. r is the position from the nucleus. Use the wave functions appropriately in Table 6-1 of the textbook. You can use the integration of x" exp(-ax) dx= a (n>-1, a>0). an+1
Calculate the expectation value of an electron in the state of n=1 and 1-0 of the hydrogen atom. r is the position from the nucleus. Use the wave functions appropriately...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
Consider a wave-packet of the form y(x) = e-x+7(204) describing the quantum wave function of an electron. The uncertainty in the position of the electron may be calculated as Ax = V(x2) – ((x))2 where for a function f(x) the expectation values () are defined as (f(x)) = 5-a dx|4(x)/2 f(x) so dx|4(x)2 Calculate Ax for the wave packet given above. (Hint: you may look up the Gaussian integral.]
(d) Compute 2m f(x) sin(3cr)d (Hint: Recall that sin2(2nnx/a)dx = f 2(2nnx/a)dx = £] COS'
(d) Compute 2m f(x) sin(3cr)d (Hint: Recall that sin2(2nnx/a)dx = f 2(2nnx/a)dx = £] COS'
in part A. We are going to find the value of Okay, so we know that the integral awful. The pdf, It should be one and in this case the integral is from 0 to 1. This is okay X cubed dx. So it is K over four X to the fourth. 0 1 plug in and subtract. So we get que over for here. So this implies that K equal four in part B. We are going to compute...
Particle in a box Figure 1 is an illustration of the concept of a particle in a box. V=00 V=00 V=0 Figure 1. A representation of a particle in a box, where the potential energy, V, is zero between x = 0 and x = L and rises abruptly to infinity at the walls. The Schrödinger equation for a particle in a box reads t² d²u Y +V(x)y = Ey 2m dx2 + (1) where ħ=h/21 , y represents the...