How can you show that ψ(x)= (sqrt(7/z))*sin ((2*pi)/(z)) is an eigenfunction of hamilition?

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How can you show that ψ(x)= (sqrt(7/z))*sin ((2*pi)/(z)) is an eigenfunction of hamilition?
A function Ψ(x) is an eigenfunction of an operator A with an eigenvalue λ if Ay(x)-AW(x) where λ is some number. Show that the function ψ(x)-xe-rn is an eigenfunction of the operator A--x2. What is the eigenvalue?
x < n with BCs y(0)= 0 and y(z) 0. (1 point) Find the eigenvalues and eigenfunctions for y" = Ay on 0 Note that any constant times an eigenfunction is also an eigenfunction. In order to obtain a unique solution find (x) so that x) dx 1 First find the eigenvalues and orthonormal eigenfunctions for n 1, i.e., An, >,(x). For n 0 there may or may not be an eigenpair. Give all these as a comma separated list....
1. Show y = sin ax is not an eigenfunction of the operator d/dx, but is an eigenfunction of the operator da/dx. 2. Show that the function 0 = Aeimo , where i, m, and A are constants, is an eigenfunction of the angular momentum operator is the z-direction: M =; 2i ap' and what are the eigenvalues? 3. Show the the function y = Jź sin MA where n and L are constants, is an eigenfunction of the Hamiltonian...
(a) Show that (@) = sin e- is an eigenfunction of both Î, and Î", where = -1 1 a 1 22 sin + sin 020 sin0 and derive the corresponding eigenvalues. You may use the identity 1 a 1 sin sin 2 sin sin 0 80 sino 31 (sin 00 (5 marks) (6) Consider the function $(,0,4)= A - 1/200 sin 6e-ip, 20 where A is a constant and an is the Bohr radius. This is a hydrogen atom...
9. Show that the function w= sin(x) (n and a are constants) is an eigenfunction of the Hamiltonian operator H = - raxz. What are the eigenvalues? hbar and m should be considered constant factors.
Could you please help me to derive the two equations below? T= 2*pi*sqrt(m/k) T=2*pi*sqrt(l/g)
• Problem 7. For a wave-function W.(x) = (2/a)" sin(x/a) calculate the average position (<x>). Is the function W.(x) = (2/a) sin(x/a) an eigenfunction of the x operator?
For y = 3 sin 2(x - pi/4) Show your work! a) Find the amplitude, period, and horizontal shift of the function b) Graph the function.
(1 point) This problem is concerned with solving an initial boundary value problem for the heat equation: (0,t)-0, t0 u,o)- in the form, ie where the term involving cy may be missing. Here y is the eigenfunction for Ay- 0 so if zero is not an eigenvalue then this term will be zero First find the eigenvalues and orthonormal eigenfunctions for n1.iA. Pa(x). For n 0 there may or may not be an eigenpair. Give all these as a comma...
Ans =sqrt(2)cos(10^7t)cos(2.5*10^5t-pi/4)
Plz show all the steps
In the circuit below, assume that 1,0) = (1 mA) cos25x 105) cos(107t). Find v (t). i (t) 10 uH 1000 pF Hint: from trigonometry, cos(a + b) = cos(a) cos(b)-sin(a) sin(b) cos(a-b) = cos(a) cos(b) + sin(a) sin(b) Adding these two equations removes the sin terms, giving cos(a + b) + cos(a-b) = 2 cos(a) cos(b) Therefore, a signal that is the product of two cosine waveforms at given frequen- cies can...