Answered: A one-particle, one-dimensional system… | bartleby

Related questions

Question

one-dimensional
A one-particle,
system has the
potential energy function V = V₁ for 0 ≤ x ≤ 1 and V =
∞ elsewhere (where Vo is a constant).
a) Use the variation function = sin() for 0 ≤ x ≤ 1
and = 0 elsewhere to estimate the ground-state
energy of this system.
b) Calculate the % relative error.

Expert Solution

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

p-7 please help me with the below problem with step by step explanation clearly.
Please asap
Problem 1. Using the WKB approximation, calculate the energy eigenvalues En of a quantum- mechanical particle with mass m and potential energy V (x) = V₁ (x/x)*, where V > 0, Express En as a function of n; determine the dimensionless numeric coefficient that emerges in this expression.
Charge is distributed over a triangular region in the xy-plane bounded by the y-axis and the lines y = 5 – x and y = 1+ x. The charge density at a point (x, y) is given by o(x, y) = x + y, measured in coulombs per square meter (C/m 2). Find the total charge. Select one: О а. 4 С b. 68 C 3 44 C 3 O c. O d. 20 37 C 3 е.
Consider a mass, m, moving under the influence of an effective potential energy -a b T 7-2 U(r) = + " where a and b are positive constants and r is the radial distance from the origin. In this case, U(r) is a 1D potential energy. (c) Expand The function for U(r) for small displacements about the equilibrium point, To. This will be a Taylor series for U(r) in terms of (r-ro)", where n is an integer. Generate the first three nonzero terms in the series.
In the region 0 w, V3 (x) = 0. (a) By applying the continuity conditions atx = a, find c and d in terms of a and b. (b) Find w in terms of a and b. -
Given the internal energy U and entropy S of N weakly interacting particles in a closed system with fixed volume V. U = NkgT² (27In 2) U S = Nkg lnz + T (a) Prove the Helmholtz free energy (b) Prove the Pressure of the system is F = -NkBT ln z P = Nk Tln z) ( T
Find C please step by step .Minimal use of the calculator please
2) Consider a particle in a three-dimensional harmonic oscillator potential V (r, y, z) = 5mw²(r² + y² + z®). The stationary states of such a system are given by ntm(r, y, z) = vn(x)¢r(y)v'm(2) (where the functions on the right are the single-particle harmonic oscillator stationary states) with energies Entm = hw(n +l+m+ ). Calculate the lifetime of the state 201.
A potential function is shown in the following with incident particles coming from -0 with a total energy E>V2. The constants k are defined as k₁ = 2mE h? h? k₂ = √√2m (E - V₁) h² k3 = √√2m (E - V₂) Assume a special case for which k₂a = 2nπ, n = 1, 2, 3,.... Derive the expression, in terms of the constants, k₁, k2, and k3, for the transmission coefficient. The transmis- sion coefficient is defined as the ratio of the flux of particles in region III to the inci- dent flux in region I. Incident particles E>V₂ I V₁ II V2 III x = 0 x = a
A real wave function is defined on the half-axis: [0≤x≤00) as y(x) = A(x/xo)e-x/xo where xo is a given constant with the dimension of length. a) Plot this function in the dimensionless variables and find the constant A. b) Present the normalized wave function in the dimensional variables. Hint: introduce the dimensionless variables = x/xo and Y(5) = Y(5)/A.
A particle experiences a potential energy given by U(x) = (x² - 3)e-x² (in SI units). (a) Make a sketch of U(x), including numerical values at the minima and maxima. (b) What is the maximum energy the particle could have and yet be bound? (c) What is the maximum energy the particle could have and yet be bound for a considerable length of time? (d) Is it possible for a particle to have an energy greater than that in part (c) and still be "bound" for some period of time? Explain. Responses

SEE MORE QUESTIONS