(WF-1) The wave function for an electron moving in 1D is given by: y(x) = C(x − ix²) for 0 ≤ x ≤ 1 and zero everywhere else. (a) Find the value of the normalization constant (C) for the wave function. (b) What is the probability of locating the electron between x = 0 and x = 1/4? (c) What is the probability of locating the electron between x = 1/4 and x = 3/4?
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- (WF-2) The wave function for a proton moving in 1D is given by: y(x) = Csin(x) for 0 ≤ x ≤ n and zero everywhere else. (a) Find the value of the normalization constant (C) for the wave function. (b) What is the probability of locating the proton between x = 0 and x = π/4? (c) What is the probability of locating the proton between x = π/2 and x = n?U = U, %3D U = 0 X = 0 A potential step U(x) is defined by U(x) = 0 for x 0 If an electron beam of energy E > U, is approaching from the left, write the form of the wave function in region I (x 0) in terms of the electron mass m, energy E, and potential energy U,. Do not bother to determine the constant coefficients. Formulas.pdf (Click here-->) Edit Vicw Insert Format Tools Table 12pt v Paragraph BIU Av eu T? vThe probability of finding a particle in differential region dx is: O W(x,t) * W(x,t) W(x,t) / W(x,t)* W(x,t)*/ W(x,t) W(x,t) + W(x,t)*
- Consider a particle with the following wave-function: ,xL and L and A are constants. (a) What is the normalization constant A (in terms of L)? (b) What is (in terms of L)? ? (ie, ) (c) What is the probability that the particle will be found within x=0 and L/2?p , For a step potential function at x = 0, the probability that a particle exists in the region x > 0 is (A) zero. (B) 1. (C) larger than zero. (D) larger than 1.Consider the following three wave functions: wi(y) = Aje¬", w2(v) = Aze-³/2, w3(y) = A3(e¬y* + ye¬³/2), where A1, A2, and A3 are normalization constants. (a) Find the constants A1, A2, and A3 so that w1, w2, and w3 are normalized. (b) Find the probability that each one of the states will be in the interval –1 < y < 1.
- The motion of electrons in a conductor is purely random in nature as the electrons do not follow a strict path to move from one location to the other. For a short burst of time, one of the electrons in a conductor being studied is identified to be moving approximately in the following manner: (a) (b) 7=(cos(zy)-x, cos(xz) — y, cos(xy) - z). Calculate the divergence of 7. Determine whether the electron has any tendency to rotate at point (0,0,0).The wavefunction for a harmonic oscillator with v= 1 is given by: y exp{-1²} y 2 Vv1 = Ny 2y exp · (x²) ¹/2 Determine the expectation value for root-mean-square position,A system of particles is in a coordinate-state ibr (x) = Nx sin 2a and zero elsewhere. (a) Find the normalization constant. (b) What is the predicted average location of the particle? (c) Evaluate the expectation value of momentum. Note: cos ac fx cos ax dx sin ax a a² S x² cos ax dx - (²-²) = cos ax + in the region -a < xV (x) = 00, V(x) = 0, x<0,x 2 a 0Consider a potential barrier defined by = U (x) T = with Uo 1.00 eV. An electron with energy E > 1 eV moving in the positive x- direction is incident on this potential. The transmission probability for this situation is given by x L 4(E/Uo) [(E/Uo) - 1] sin² [√2m(E – U₁)L/ħ] + 4(E/U₁) [(E/U₁) − 1] It is found that the reflection probability is zero for E = 1.10 eV and non-zero for smaller incident energies. What is the width of the potential barrier L?Consider a one-dimensional particle which is confined within the region 0≤x≤a and whose wave function is (x, t) = sin (x/a) exp(-iwt). (D) v sv (a) Find the potential V(x). (b) Calculate the probability of finding the particle in the interval a/4 ≤x≤3a/4.SEE MORE QUESTIONSRecommended textbooks for youUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax