A particle with the energy E is incident from the left on a potential step of height Uo and a delta-functional peak at r = 0: U (x) = 0, I <0 U (x) = Uo + V 8(x), Calculate the transmission and reflection coefficients at the energies E > Uo
Q: Find the energy of plane wave function exp i (kx-wt)
A: Given, Wave function, ψ=eikx-wt
Q: Calculate the transmission and reflection coefficients for an electron with kinetic energy 8 eV and…
A: Given data- The initial kinetic energy of the electron is E0=8 eV =12.8×10-19 J The potential…
Q: Consider the quantum-mechanical scattering problem in the presence of inelastic scattering. Suppose…
A:
Q: In partial wave analysis of scattering, one has to consider waves with L= 0, 1, 2, 3, For a given…
A: To answer: In the partial wave analysis of scattering one has to consider waves with L=0,1,2,3. The…
Q: Calculate the uncertainties dr = V(r2) and dp = Vp?) for a particle confined in the region -a a, r…
A: As we can see the given wave function is normalised and in outside region it's zero. Therefore This…
Q: As a 1-dimensional problem, you are given a particle of mass, m, confined to a box of width, L. The…
A:
Q: Calculate the period of oscillation of ?(x,t) for a particle of mass 1.67 × 10-27 kg in the first…
A: Given: m=1.67×10-27kg, a=1.68×10-15m The energy of a particle in a box of width a is defined by :…
Q: The displacement x of a classical harmonic oscillator as a function of time is given by x= A…
A: The probability ω(ϕ)dϕ that ϕ lies in the range between ϕ & ϕ+dϕ is then simplyω(ϕ)dϕ=(2π)-1dϕWe…
Q: The wave function of free particle initially at time t=0 is given by the wave packet (x,0) =…
A:
Q: An electron has a kinetic energy of 12.6 eV. The electron is incident upon a rectangular barrier of…
A:
Q: Consider a potential barrierV(x) = {0, xVo, find the transmission coefficient, T
A:
Q: Q4: A purticle of mass m and kinetic energy E>0 approuches potential drop V. Find the reflected and…
A:
Q: A particle of mass m moves inside a potential energy landscape U (2) = X|2| along the z axis. Part…
A: To determine the units of the constant λ, we can use the given formula for potential energy U(z) and…
Q: Find the normalize constant A and the average value of the kinetic energy of a particle in box has…
A:
Q: By considering the integral ∫02π cosmlϕ cosm'lϕ dϕ, where ml≠m'l ,confirm that the wavefunctions…
A: Normalize the wavefunction…
Q: We have a free particle in one dimension at a time t = 0, the initial wave function is V (x,0) = Ae…
A:
Q: We have a free particle in one dimension at a time t = 0, the initial wave function is V (x, 0) =…
A: To answer the question, we first write the Normalization condition for a wave function, and then use…
Q: Problem 1: The wavefunction for a particle is shown below. (a) What is the normalization constant A?…
A:
Q: b): In partial wave analysis of scattering, one has to consider waves with L= 0, 1, 2, 3, For a…
A: Partial wave expansion is dominated especially at low energies, i.e. by small l The orbital…
Q: im@ Find the expectation Value (L₂) of the wave function 10-e' and prove the ² Where Lz - ih == Ә…
A:
Q: (WF-3) Consider the two normalized wave function shown below. Calculate the expectation value for…
A:
Q: Evaluate the following expectation values: (a) ⟨ℓ,m1∣Lx∣ℓ,m2⟩ (b) ⟨ℓ,m1∣Ly∣ℓ,m2⟩
A:
Q: Consider a particle with 1-D wave-function (x) = kexp(-x²). Sketch (x),
A:
Q: Evaluate the equation of continuity of plane wave function Exp i (kx-wt).
A: Given, Plane wave function,ψ=eikx-wt
Q: A particle is confined to a 1D box between x=0 and x=1 and has the normalized wavefunction of 105 V…
A:
Q: Show that is a solution to the time-independent Schrödinger equation, with potential V(x) = 2h²² and…
A: Given: The potential of the particle is Vx = 2 ħ2 m x2 The energy Eigenvalue of the particle is E =…
Q: A Free Particle moving with a wave fanction 4 = Ae -ix² on a specified Path from 0 to 0.5 on the X…
A:
Q: What would happen to the incident wave (x) = Ae¹kx at x < 0 that sees a step potential in the form…
A: a) Incident wave function is, ψx=Aeikx at x<0 Potential is, Vx=iΓ Here, i is complex and…
Q: Consider a particle of mass m moving in one dimension with wavefunction $(x) Vi for sin L - and zero…
A: The momentum operator is given by Therefore the operator is given by Where The given wave…
Q: In a scattering experiment, the potential is spherically symmetric and the particles are scat- tered…
A: The scattering amplitude is given by, f(θ)=1k∑l=0l=∞(2l+1)eiδlsinδlPlcosθ For the s wave, l=0 For…
Q: n partial wave analysis of scattering, one has to consider waves with L= 0, 1, 2, 3, For a given…
A: Concept used: Any particle getting scattered through potential is described as plane wave. In…
Q: Consider the wavefunction (4.5) with mi an integer and o < ¢< 2m. Find the normalization factor for…
A:
Q: Let y, (x) denote the orthonormal stationary states of a system corresponding to the energy En.…
A: Expectation value of energy
Q: Use the time-dependent Schroedinger equation to calculate the period (in seconds) of the…
A: Mass of particle m = 9.109 × 10− 31 kg Width of the box a = 1.2 ×10− 10 m
Q: We have a free particle in one dimension at a time t 0, the initial wave function is V(x,0) =…
A:
Q: In the region 0 w, /3 (x) = 0. (a) By applying the continuity conditions at.x = a, find c and d in…
A: Given that the wavefunction of a particle is , ψ1x=-bx2-a2 0≤x≤aψ2x=x-d2-c…
Q: Evaluate , , △x, △px, and △x△px for the provided normalized wave function
A:
Q: S-U. 10. -U, -c<r <c %3D otherwise
A: Given wave function as, ψ(x)=a(b+x);-b<x<0a(b-x);0<x<b0;otherwise
Q: The Maxwellian distribution of speeds in 3d is maybe written as n is the particle number density…
A: 1. Average speed is,…
Q: Like a harmonic oscillator with a orce constant of 1550 N/m of the nitrogen oxide molecule suppose…
A:
Step by step
Solved in 2 steps
- Calculate the phase shift 8 (K) for the S-wave scattering (1-0). Assume that the potential is given as the delta - Shell 2 U (0)_ _h² 2m S(x-a)You are given a free particle (no potential) Hamiltonian Ĥ dependent wave-functions = -it 2h7² m sin(2x) e = V₁(x, t) V₂(x, t) 2 sin(x)e -ithm + sin(2x)e¯ What would be results of kinetic energy measurements for these two wave-functions? Give only possible outcomes, for example, it is possible to get the following values 5, 6, and 7. No need to provide corresponding probabilities. ħ² d² 2m dx2 and two time- -it 2hr 2 mAn 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?
- Be-H is given -ur In the Born approximation, the scattering amplitude f(e) for the Yukawa potential V(r) = by: (in the following b = 2k sin E = h?k? / 2m) 2 | 2mß 2mß 2mß 2mB (a) (b) (c) (d) h? (u? +b?)Calculate the uncertainties dr = V(x2) and op = V(p²) for %3D a particle confined in the region -a a, r<-a. %3Di need the answer quickly
- = = An electron having total energy E 4.60 eV approaches a rectangular energy barrier with U■5.10 eV and L-950 pm as shown in the figure below. Classically, the electron cannot pass through the barrier because E < U. Quantum-mechanically, however, the probability of tunneling is not zero. Energy E U 0 i (a) Calculate this probability, which is the transmission coefficient. (Use 9.11 x 10-31 kg for the mass of an electron, 1.055 x 10-34] s for h, and note that there are 1.60 x 10-19 J per eV.) (b) To what value would the width L of the potential barrier have to be increased for the chance of an incident 4.60-eV electron tunneling through the barrier to be one in one million? nm(Mathematical method for physics)The expectation value of a function f(x), denoted by (f(x)), is given by (f(x)) = f(x)\(x)|³dx +00 Yn(x) = where (x) is the normalised wave function. A one-dimensional box is on the x-axis in the region of 0 ≤ x ≤ L. The normalised wave functions for a particle in the box are given by -sin -8 Calculate (x) and (x²) for a particle in the nth state. n = 1, 2, 3, ....
- Calculate the tunneling probability when the kinetic energy of the particle is 0.2 MeV, the barrier height is 20 MeV, the probability amplitude is 1.95×10¹5 m²¹, and the width of the barrier is 2.97x10-¹8 m. (A) 0.046 (B) 0.156 (C) 0.026 (D) 0.456Consider 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…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.