Answered: f1, f2, f3, and f4 are eigenfunctions… | bartleby

Related questions

Question

f1, f2, f3, and f4 are eigenfunctions of the operator A, with
corresponding eigenvalues c1, c2, C3, and c4 The system is
described by the normalised wavefunction (4):
1
Y = f1 – if2 + 3f3 +fA
Determine the outcome of measuring the observable
(Y|A|Y)
Assume that the eigenfunctions f1, f2, f3, and f4, are
orthogonal and normalised.

Expert Solution

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

a particle is confined to move on a circle's circumference (particle on a ring) such that its position can be described by the angle ϕ in the range of 0 to 2π. This system has wavefunctions in the form Ψm(ϕ)= eimlϕ where ml is an integer. Show that the wavefunctions Ψm(ϕ) with ml= +1 and +2 are ORTHOGONAL Show full and complete procedure. Do not skip any step
Show that Â Â for any operator Â is positive.
Consider the following operators on a Hilbert space V³ (C): 0-i 0 ABAR-G , Ly i 0-i , Liz 00 √2 0 i 0 LE √2 010 101 010 What are the corresponding eigenstates of L₂? 10 00 0 0 -1 What are the normalized eigenstates and eigenvalues of L₂ in the L₂ basis?
a2 Laplacian operator 72 = ax? ay? T əz2 in spherical polar coordinates is given by az? p² = () 1 a 1 1 a2 r2 sin e ae sin 0-) is an eigenfunction of the Laplacian operator and find the +- r2 sin 0 a0 r2 ar ar. r2 sin? 0 a20 sin 0 sin o Show that function r2 corresponding eigenvalue.
Plot the first three wavefunctions and the first three energies for the particle in a box of length L and infinite potential outside the box. Do these for n = 1, n = 2, and n = 3
please provide detailed solutions for a to d. thank you!
Suppose that the wave function for a system can be written as 4(x) = √3 4 · Φι(x) + V3 2√₂ $2(x) + 2 + √3i 4 $3(x) and that 1(x), 2(x), and 3(x) are orthonormal eigenfunc- tions of the operator Ekinetic with eigenvalues E₁, 2E₁, and 4E₁, respectively. a. Verify that (x) is normalized. b. What are the possible values that you could obtain in measuring the kinetic energy on identically prepared systems? c. What is the probability of measuring each of these eigenvalues? d. What is the average value of Ekinetic that you would obtain from a large number of measurements?
In the operator eigenvalue equation, Af(x) =a f(x), which of the following statements is not true? the effect of the operator, A, on f(x) is to increase its magnitude by a factor of a Omultiples of f(x) would be eigenfunctions of the operator, A Of(x) is an eigenfunction of the operator, A the number, a, must be equal to 0 or 1 OOO O
Consider the following operator imp Â= and the following functions that are both eigenfunctions of this operator. mm (0) = e² ‚ (ø) = (a) Show that a linear combination of these functions d² dø² is also an eigenfunction of the operator. (b) What is the eigenvalue? -m imp c₁e¹m + c₂e² -imp -imp = e
Consider a particle moving in a 2D infinite rectangular well defined by V = 0 for 0 < x < L₁ and 0 ≤ y ≤ L2, and V = ∞ elsewhere. Outside the well, the wavefunction (x, y) is zero. Inside the well, the wavefunction (x, y) obeys the standing wave condition in the x and y direction, so it is given as: where A is a constant. (x, y) = Asin(k₁x) sin(k₂y), (a) The wavenumber k₁ in the x direction is quantized in terms of an integer n₁. Using the standing wave condition, find the possible values of k₁. (1) (b) The wavenumber k2 in the y direction is quantized in terms of a different integer n₂. Using the standing wave condition, find the possible values of k₂. (1) (c) Each state of the 2D infinite rectangular well is defined by the pair of quantum numbers (n₁, n₂). What is the energy of the state Eni,n₂? JXZ1