Show that the two wavefunctions: Are orthogonal COS

Question

Question

Show that the two wavefunctions: Are orthogonal

$COS$

$Y_{2}(\Theta ,\phi )=(\frac{5}{16\pi})^{^{1/2}}(3\cos^{2}\Theta -1)$

science Advanced-Physics

Answer 1

Answer #1

$Given wavefunctions are Consi der 15 447T V15 (0)(27) -0 Therefore, the wavefunctions Y\ and Y, are orthogonal$

Answer 2

Similar Homework Help Questions

Show that the wavefunctions , where n ≠ m, are orthogonal for a particle confined to...

Show that the wavefunctions , where n ≠ m, are orthogonal for a particle confined to the region -infinity ≤x ≤ infinity Please show all work for full credit. The following wavefunctions are from the 1-D harmonic oscillator problem (imits from - infinity to + infinity, variable is x) I. (5 pts) Show V2 is orthogonal to vs. 1a
Demonstrate that all 1-D PIB wavefunctions are orthogonal.

Demonstrate that all 1-D PIB wavefunctions are orthogonal.
3) Show that the u(2,1,1) and u(2,0,0) wavefunctions are orthogonal. AY 1 (2,1, 1)= Z ge...

3) Show that the u(2,1,1) and u(2,0,0) wavefunctions are orthogonal. AY 1 (2,1, 1)= Z ge h sin 0e tip (64T) ао 3/ 1 Z (2,0,0) (2-о)e % (32л)* (а,

Show that the wafunctions sin "/C and cos "2* are orthogonal over the interval 0sxsa. n...

Show that the wafunctions sin "/C and cos "2* are orthogonal over the interval 0sxsa. n is an integer and cOS_ are
Problem 5 (a) Two (unnormalized) excited state wavefunctions of the H atom are (1) 4 =...

Problem 5 (a) Two (unnormalized) excited state wavefunctions of the H atom are (1) 4 = (2-)e-r/ao (ii) W = r sinô coso e-r/220 Normalize both functions to be 1. (b) Confirm that these two functions are mutually orthogonal
Determine whether the given matrix is orthogonal. If it is, find its inverse. cos sin cos...

Determine whether the given matrix is orthogonal. If it is, find its inverse. cos sin cos sin A = [ cose sin e sin e 0 cos e - cos ]

show that 9- a) A is orthogonal if and only if A' is orthogonal b) A is orthogonal if and only if A is orthogonal c) A& B are orthogonal then AB is orthogonal d) A is orthogonal then det(A)=1...

show that 9- a) A is orthogonal if and only if A' is orthogonal b) A is orthogonal if and only if A is orthogonal c) A& B are orthogonal then AB is orthogonal d) A is orthogonal then det(A)=1 or det(A)=-1 9- a) A is orthogonal if and only if A' is orthogonal b) A is orthogonal if and only if A is orthogonal c) A& B are orthogonal then AB is orthogonal d) A is orthogonal then det(A)=1...
6.2(a) Complex functions of the form eikx can be used to model the wavefunctions of particles...

6.2(a) Complex functions of the form eikx can be used to model the wavefunctions of particles in a linear accelerator. Show that any linear combination of the complex functions e2ix and e−2ix is an eigenfunction of the operator d2/dx2 and identify its eigenvalue. 6.2(b) Functions of the form sin nx can be used to model the wavefunctions of electrons in a carbon nanotube. Show that any linear combination of the functions sin 3x and cos 3x is an eigenfunction of...
Show that if A and B are orthogonal matrices, then A B is an orthogonal matrix.

Show that if A and B are orthogonal matrices, then A B is an orthogonal matrix.

4. We saw in class that if A is an orthogonal matrix, then ||AX|| = ||X||....

4. We saw in class that if A is an orthogonal matrix, then ||AX|| = ||X||. One matrix for which we know this is true is the rotation matrix, A = [cos – sin 0] sin cos a. (2 pts) Show that A is an orthogonal matrix. b. (2 pts) Since A is an orthogonal matrix, A-1 = AT. Show that AT can be written as cos 0 – sino w does the angle o relate to the angle ?...