What is the probability that the particle in a box will be found in the region in the states and ? What is the classical value expected?
What is the probability that the particle in a box will be found in the region...
8. A particle in a box (0x<L) has wave functions and energies of En 8m2 a) Normalize the wave functions to determine A b) At t-0, ψ(x)-vsv, + ψ2 . 2. c) The particle will oscillate back and forth. Derive an expression for the oscilla- tion frequency in terms of h, m, and L Derive expressions for Ψ(x, t) and |Ψ(x, t)
5. Given the probability density f(x)= for -0<x<00, find k. 1+ 2 Jor -
A particle is in the ground state of a symmetric infinite square well with Vx) O for -a/2<x<+a/2, and infinite elsewhere. (a) The well then undergoes an instantaneous symmetric expansion to -a <<< ta. Calculate the probabilities of the particle being found in each of the three lowest energy states of the larger well. (b) Instead, suppose that the well expansion takes place adiabatically. Again, calculate the probabilities of the particle being found in each of the three lowest energy...
Need Help!! Physic Problem part 1-4 An electron in a region in which there is an electric field experiences a force of <5 x 10-17,-1.5 x 10-16-35 x 1016, N. What is the electric field at the location of the electron? (Express your answer in vector form.) o16, -3.5 x 1016> N. What is the 0.3905 0.911 N/C What is the electric field at a location b0.3, 0.3, -0.6> due to a particle with charge +7 nC located at <0.1,...
7. For the probability density function f(x) = for 0 <<<2 (a) Find P(x < 1) (b) Find the expected value. (c) Find the variance.
Explain ng on the particle as a function of x, for O <x < 7 meters?
In solving the particle in a one dimensional infinite depth box problem (0k x < a) we started with the function following is a true statement? (a) The value of k is found by requiring that the solution be normalized. (b) The function wx) is not an eigenfunciton of the operator d2/dx2 (c) It is necessary that this function equals a when x=0 (ie, Ψ(0) = a). (d) The boundary condition at x = 0 is used to show that...
3. A particle of mass m in a one-dimensional box has the following wave function in the region x-0 tox-L: ? (x.r)=?,(x)e-iEy /A +?,(X)--iE//h Here Y,(x) and Y,(x) are the normalized stationary-state wave functions for the n = 1 and n = 3 levels, and E1 and E3 are the energies of these levels. The wave function is zero for x< 0 and forx> L. (a) Find the value of the probability distribution function atx- L/2 as a function of...
3,40 A random variable X has probability density function fx(x) = 1 0<x< 1. Find the probability density function of Y = 4x3 - 2.
(15) 4. The state of the particle-in-a box located between 0<x<a is described by the following normalized wavefunction at t=0: Y(x,t=0) =(1/2) A Sin (fx/a)-(1/12) A Sin(3 rex/a) + (1/2) A Sin(5tx/a) (10) a) If the energy of the system is measured at t=0, what energies will be observed What is the probability (in percent) of observing an energy E> 9h-/8ma?? on