Given initial wave function:
m=
length=a=0.02nm=
Let us find expectation value of momentum first then we will check its amplitude and frequency
We know
Hence
As
Hence
As all functions are SINE which are odd functions whose integration is zero .i.e= if f(x) is odd
Hence
Hence amplitude of expectation value of momentum is zero and frequency if we take as COSINE function is where n=1,2,.... for SINE function it is
With what amplitude and frequency does the expectation value of the momentum of a proton (m=1.67x10-27...
2. A particle of mass m in the infinite square well of width a at time 1 - 0 has wave function that is an equal weight mixture of the two lowest n= 1,2 energy stationary states: (x,0) - C[4,(x)+42(x)] (a) Normalize the wave function. Hints: 1. Exploit the orthonormality of W, 2. Recall that if a wave function is normalized at t = 0, it stays normalized. (b) Find '(x, t) and (x,1)1at a later time 1>0. Express Y*...
##### show all steps thoroughly (sorry for my bad grammar) Assume that electron in area electric field of proton and in the state wave function r + 2p2 1,0.0 1) Find expectation value of energy 2) Find expectation value of angular momentum squared (L2) 3) Find expectation value of angular momentum in component axis -Z L) 4) How much angular momentum in component axis-Z will probability of found particle? And why? Assume that electron in area electric field of proton...
A proton (mass 1.67x10^-27 kg, charge 1.6x10^-19C) travels at 10^4 m/s to the left through a uniform magnetic field of magnitude 0.2 T, which points up toward the top of the page. A) What is the magnitude of the force on the proton? B) what is the direction of the force on the proton? ( into page, out of page, right, or left)
Problem 4 For the wave function φ(x,0) = Ax(a-x) find the expectation value of Hat time ț-0 in the ID box of length .
A transverse wave with an amplitude of 6 m, a frequency f=6.7 Hz , and a wavelength λ=6 m is traveling down a taut string. If the wave equation describing the displacement of the string at position x and time t is given by y(x,t)=Asin(kx−ωt) a.) what are the parameters A, k, and ω? b.) What is the speed of the wave traveling down the wire? m/s c.) If the tension in the wire is measured to be 6 N,...
A plane electromagnetic wave, with wavelength 2.4 m, travels in vacuum in the positive direction of an x axis. The electric field, of amplitude 390 V/m, oscillates parallel to the y axis. What are the (a) frequency, (b) angular frequency, and (c) angular wave number of the wave? (d) What is the amplitude of the magnetic field component? (e) Parallel to which axis does the magnetic field oscillate? (f) What is the time-averaged rate of energy flow associated with this...
A transverse wave on a string has an amplitude of 0.25 m and a frequency of 183 Hz. Consider the particle of the string at x = 0 m. It begins with a displacement of y = 0 m when t = 0 s, according to the following. y = A sin 2πft − 2πx λ y = A sin 2πft + 2πx λ How much time passes between the first two instants when this particle has a displacement of...
Question # 7: Determine the numerical value of the square of the momentum motion for the particle in 1D box. (Hint: suppose that the square of the momentum of motion is a sharp property (until the reverse is proved!) (Answer: P: P =+ Question # 8: Calculate the degree of uncertainty in the momentum of motion and in the speed of a. Electron moves in a box of length 18. b. A hydrogen atom moves in a box of length...
A plane electromagnetic wave, with wavelength 2.8 m, travels in vacuum in the positive direction of an x axis. The electric field, of amplitude 300 V/m, oscillates parallel to the y axis. What are the (a) frequency, (b) angular frequency, and (c) angular wave number of the wave? (d) What is the amplitude of the magnetic field component? (e) Parallel to which axis does the magnetic field oscillate? (f) What is the time-averaged rate of energy flow associated with this...
A proton (rest mass is 1.673 times 10^-27 kg, rest energy is 938.3 MeV) has kinetic energy of 2500 MeV. find its momentum (in kg-m/s) (use relativistic relations) find its wavelength if one measures the proton's position to an uncertainty delta x of + l-5.60 times 10^-14 m. find the minimum possible uncertainty in the proton's momentum A panicle of mass 6.646 times 10^-27 kg is confined to a one-dimensional box of length 3.0 times 10^-14 m. What wavelength photon...