Answered: 26. Use the Fourier transform method to… | bartleby

Related questions

Question

26. Use the Fourier transform method to show that the solution of the
one-dimensional Schrödinger equation for a free particle of mass m,
ihube
-00 < x < 0,
t > 0,
2m
V (x, 0) = f (x),
-00 < x < ∞,
where y and Vr tend to zero as |x| → 0, and h = 2nh is the Planck
constant, is given by
1
v (x, t) = f(£)G(x- £) d£,
where G (x, t) =
(1-i
25
is the Green's function and y=
exp
4iyt
2m

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

: In class we did a problem where we saw that Planck’s law, which is given byI(λ, T) = 2πhc2λ5(ehc/λkbT − 1),at high wavelengths reduces to the classical predictionI(λ, T) = 2πckBTλ4.We did this by using the MacLaurin series for an exponential.1 + x +x22! +x33! +x44! + ...When we did this problem in class, we reasoned that,when the wavelength (λ) is large, the term hc/λkbTis small enough that any term (hc/λkbT)2 or (hc/λkbT)3 or any higher power is neglible. That’s how weshowed that, in the limit of large λ, Planck’s law reduces to the classical prediction. Now assume that wewant to make a slightly better approximation. We still assume that λ is large and therefore (hc/λkbT)3 and(hc/λkbT)4 and all higher powers are negligible, but now we want to work at the level of precision where(hc/λkbT)2is not negligible. What does Planck’s law reduce to in this case?
(b) Calculate the de Broglie wavelength of an electron having a mass of 9.11 x 10-31 kg and a charge of 1.602 x 10-19 J with a Kinetic energy of 110 eV. The value of the Planck’s constant is equal to 6.63 * 10-34 Js.
Calculate the de Broglie wavelength of an electron moving with 1/3rd of the speed of light in vacuum. (Neglect relativistic effect) (Planck's constant : h = 6.63 × 10-34 Js, Mass of electrons : m = 9.11 × 10-28 g) %3D
O https://www-awu.aleks.com/aiek ROEqmvAnknhdcHJmAch Blackbody b Answered: Decide. Convert grams Calc... * Convert hertz (Hz] t. G VidQuiz: Trans. In B... Syllabus: 1A Blake F O ELECTRONIC STRUCTURE AND CHEMICAL BONDING Understanding the meaning of a de Broglie wavelength Imagine an alternate universe where the value of the Planck constant is 6.62607 J·s. In that universe, which of the following objects would require quantum mechanics to describe, that is, would objects would act like everyday objects, and be adequately described by classical mechanics? object quantum or classical? A car with a mass of 1100. kg, 4.0 m long, moving at O classical 112.0 km/h. O quantum A grain of sand with a mass of 205 mg, 795. um wide, moving at 6.00 mm/s. O classical O quantum An eyelash mite with a mass of 13.6 ug, 205 um wide, moving at 29. um/s. O classical O quantum An atom with a mass of 1.0 x 10-25 kg, 56. pm wide, moving at 222. m/s. O classical O quantum Explanation Check 72022 McGraw Hill…
3) Determine the energy of a photon emitted when an electron relaxes from the excited state ν=4 to ground state ν=1 of a harmonic oscillator if the force constant κ is 285 N m–1.
= 1. Photoelectric effect. In a photoelectric experiment in which monochromatic light of wave- length \ falls on a potassium surface, it is found that the stopping potential Vstop is 1.9 V for > 300 nm and 0.88 V for \ = 400 nm. Imagine we know neither Planck's constant, nor the workfunction for potassium, nor the threshold frequency fo. But assume we do know the elementary charge e 1.60 × 10-19 C and want to test the theoretical prediction of Eintsein's theory. = (a) From the given data, calculate a value for Planck's constant, h. (b) From the same data, find the workfunction Eo and the threshold frequency fo for potas- sium. (c) Then compare your results for h and Eo to their known values (see Knight, Table 38.1 for the work function). (d) Plot eVstop as a linear function of frequency f. Include the information you have found in parts (a) and (b) as well as the experimental data.