A particle of mass m is in a harmonic oscillator potential with angularfrequency o. It is in the state u(x) = (3u{n=1}(x) + 4u{n=3}(x))/5).a. Give the result of a single measurement of the energy.b. Give the expectation value of the energy.c. Give the expectation value of the momentum.d. Give the result of a single measurement of the momentum. Hint: Average energyis shared equally between the kinetic and potential energy for a simple harmonicoscillator.

(a) Given: The mass of the particle is m. The angular frequency is ω. The state in which the…

Answered: A particle of mass m is in a harmonic…

Similar questions

2. A wave function is a linear combination of 1s, 2s, and 3s orbitals: y(r) = N(0.25 y,s + 0.50W2, +0.30W). Find the normalization constant N, knowing that 1s, 2s, and 3s orbitals are normalized.
The potential curve and the spacing between the allowed energies of a quantum oscillator are shown in the figure. If the spring stiffness is increased, the result will be: Ground state Select one: O a. Narrower potential curve and smaller spacing between the allowed energies O b. Narrower potential curve and larger spacing between the allowed energies. O c. Wider potential curve and larger spacing between the allowed energies. Od. Wider potential curve and smaller spacing between the allowed energies /mod/quiz/atte php?tts coram Energy
2. A particle is confined to the x-axis between x = 0 and x = 3a. The wave function of the particle is = Ax sin (5x). a. b. Determine (x) without determining A. Determine ² = ((x - (x))²) without determining A.
In which situation's would angular acceleration be negative? Select all that apply 1. An object is at rest and is starting to rotate clockwise 2. An object is rotating clockwise and speeding up 3. An object is rotating clockwise and speeding up 4. An object is rotating counterclockwise and slowing down
1. Particle in a Box. A particle of mass m that is confined in a one- dimensional box of length L, i.e. x € (0, L), is described by the wave function: v (2, 1) = A sin (17²) exp[i Ent], t) where En OYes n²π²ħ² 2mI² 9 where n E N where n E N. The wave function is zero outside the box. Calculate the normalization constant A and compute the uncertainty of position and momentum regardless of the quantum number n. Does it follow the uncertainty principle? ONO
10. A particle is represented (at time t = 0) by the wave function ¥(x,0) = {4(a² ¯ 0, JA(a²-x²), if- a ≤x≤+a otherwise (a) Determine the normalization constant A. (b) What is the expectation value of x (at time t = 0)? d (c) What is the expectation value of p (at time t = 0)? (Note that you cannot get it from p = m² .Why dt not?) (d) Find the expectation value of x². (e) Find the expectation value of p².
Let Vx/312 is a nomalized wave function for 0 < x < V6L what is the probability of a particle lies between 0 < x < L? A. 3.3 %. В. 16.6% С. 25.0%. D. 100.0 %. А. В. OD.
A non-isotropic harmonic oscillator has wi = W, W2 w, w2 = ;w, w3 = 2w. Its energy levels up to the fourth excited state level in terms of hw are Select one: О a. 1.75, 2.75, 3.75, 4.75, 5.75 Ob. Оь. 1.75, 2.5, 3.25, 4.0,4.5 с. 1.5,2.5, 3.5, 4.5,5.5 O d. 1.5, 1.75, 2.25, 3.5, 3.75 e. 1.75, 2.25, 2.75, 3.25, 3.75
1. A particle is confined to the x-axis between -SxSn is described by the wavefunction y(x)=1 31+cos.x (a) Normalize the wavefunction (b) Calculate the expectation value of x
Consider a particle in a 2-D box having Lx = 10 nm and Ly = 10 nm. a) Make a surface plot of all the wave functions for the first and second energy levels. b) What is the degeneracy of the second energy level? Compare and contrast the wave functions of the second energy level. c) How does the number of nodes in the x-coordinate change as n increases? How does the number of nodes in the y-coordinate change as n, increases? d) Explain whether or not those same states would be degenerate if Lx = 10 nm and Ly = 15 nm.
The kinetic energy operator in 3-D is: O a. O b. Î=- T= OCT=- O d. T= ħ 2m ħ 2m 2 2 ħ 2m ħ 2m D2 D2 For a given quantum particle (p²)=a²ħ² and : = 0. The uncertainty in momentum for this particle is: ○a. a ²ħ² Ob.aħ О с. 2а ћ O d.-aħ

A particle of mass m is in a harmonic oscillator potential with angular frequency o. It is in the state u(x) = (3u{n=1}(x) + 4u{n=3}(x))/5). a. Give the result of a single measurement of the energy. b. Give the expectation value of the energy.