Consider a wave packet which at t = 0 has the form (x,0) = Aeipox/ħe¯|x|/L Normalize (x, 0).
Q: Find the energy of plane wave function exp i (kx-wt)
A: Given, Wave function, ψ=eikx-wt
Q: What is the actual transmission probability (in %) of an electron with total energy 1.593 eV…
A: The energy of the electron E = 1.593 eV Potential barrier height Vo = 3.183 eV Width of the…
Q: dimensional wave packet at time t=0 (k)=0 for k
A: The wave function is given as:
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A: We can solve this problem by normalising Condition as following.
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A: The normalized wave function for a state is given by
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A: Given: Need to explain the wave packet be formed from a superposition of wave functions of the type…
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A: To find the Z-transform of the given function, we can first write the function in terms of the…
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Q: 07) Normalize the wave functions: A) BY Y(x)=N(2A
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Q: An electron has a kinetic energy of 12.6 eV. The electron is incident upon a rectangular barrier of…
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Q: Consider a potential barrierV(x) = {0, xVo, find the transmission coefficient, T
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Q: Normalize the wavefunction re-r/2a in three-dimensional space
A: Solution The wavefunction re-r/2a in the three dimensional space is given by
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A: Given: F(x1,x2) = ex1+x2G(x1,x2) = x2ex1 + x1ex2H = F(x1,x2) - F(x2,x1)
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A: Normalize the wavefunction…
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Q: A particle with the energy E is incident from the left on a potential step of height Uo and a…
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Q: (WF-1) The wave function for an electron moving in 1D is given by: y(x) = C(x − ix²) for 0 ≤ x ≤ 1…
A: givenΨ(x)=C(x-ix2) for 0≤x≤1Ψ(x)=0 else…
Q: Evaluate the equation of continuity of plane wave function Exp i (kx-wt).
A: Given, Plane wave function,ψ=eikx-wt
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A: To find the answer, we first write the expression for expectation value of "x" and substitute the…
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Q: Show that in a homogeneous string v = sqr(T/μ)
A: In a homogeneous string v = sqr(T/μ)
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A: We have given Maxwell's distribution
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A: Time-Independent Schrodinger equation: The time-independent Schrodinger equation in one dimension…
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Q: Q.18. Verify the statement in the text that, if the phase velocity is the same for all wavelengths…
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- Consider a particle in one-dimension. In quantum mechanics, we require µ(x,t)l´ dx to be finite. Why? If this is true, we call the wavefunction admissible.An electron has a kinetic energy of 13.3 eV. The electron is incident upon a rectangular barrier of height 21.5 eV and width 1.00 nm. If the electron absorbed all the energy of a photon of green light (with wavelength 546 nm) at the instant it reached the barrier, by what factor would the electron's probability of tunneling through the barrier increase?Suppose we had a classical particle in a frictionless box, bouncing back and forth at constant speed. The probability density of the position of the particle in soma box of length L is given by: 0 ans-fawr (7) p(x)= 0 x L a. Sketch the probability density as a function of position b. What must A be in order for p(x) to be normalized? Remember that you are welcome to use resources to solve integrals such as Wolfram Alpha, a table of integrals etc.
- The normalization condition for a wavefunction Ψ(x, t) is given by � ∞ −∞ Ψ∗(x, t)Ψ(x, t)dx = 1. This necessarily means that the LHS has to be independent of time. Show that this is indeed the caseDetermine the probability distribution function in the phase space for a relativistic particle in a volume V and with energy ε(p) = √√√/m²c²+p²c², where p is the ab- solute value of the momentum, m the mass, and c the speed of light. Give the final result in terms of the modified Bessel functions r+∞ Ky (z) = ™ (v-1)! 2 -zcosht e cosh (vt) dt Ky(z) ~ Check what happens in the limit ² →0. mc² kT z 0.Suppose that in a certain system a particle free to move along one dimension (with 0 ≤ x ≤ ∞) is described by the unnormalized wavefunction Ψ(x)=e-ax with a = 2 m−1. What is the probability of finding the particle at a distance x ≥ 1 m?
- Please helpConsider the one-dimensional step-potential V (x) = {0 , x < 0; V0 , x > 0}(a) Calculate the probability R that an incoming particle propagating from the x < 0 region to the right will reflect from the step.(b) Calculate the probability T that the particle will be transmitted across the step.(c) Discuss the dependence of R and T on the energy E of the particle, and show that always R+T = 1.[Hints: Use the expression J = (-i*hbar / 2m)*(ψ*(x)ψ′(x) − ψ*'(x)ψ(x)) for the particle current to define current carried by the incoming wave Ji, reflected wave Jr, and transmitted wave Jt across the step.For a simple plane wave ψ(x) = eikx, the current J = hbar*k/m = p/m = v equals the classical particle velocity v. The reflection probability is R = |Jr/Ji|, and the transmission probability is T = |Jt/Ji|. You need to write and solve the Schrodinger equation in regions x < 0 and x > 0 separately, and connect the solutions via boundary conditions at x = 0 (ψ(x) and ψ′(x) must be…Calculate the average or expectation value of the position of a particle in a one-dimensional box for n=2.
- Q.3) (30 Points) For the harmonic oscillator, the position and momentum operators are given by (a* + a) and p = i 2mw mwh (a*- a¯), respectively. X = Using the relations a* |n) = Vn + 1 |n + 1) and a |n) = Vn |n – 1); a) Find the expectation value of (xp). (n|xp|n) =? b) Find the expectation value of (x³). (n|x3|n) =? Please answer questions by showing all steps in your calculations clearly and easy to read and understandable.A particle with the velocity v and the probability current density J is incident from the left on a potential step of height Uo, that is, U (x) = Uo at r > 0 and U(x) = 0 at r 0.