If the particle in the box in the second excited state(i.e. n=3), what is the probability P that it is between x=L/2 and x=L/3 ?
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If the particle in the box in the second excited state(i.e. n=3), what is the probability P that it is between x=L/2 and x=L/3 ?
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- A particle has a wave function y(r)= Ne¯u , where N and a are real and positive constants. a) Determine the normalization value N. b) Find the average value of y c) Obtain the dispersion (Ar)? Note, you can use dz =r'(n+1) = n!An electron is trapped in a region between two infinitely high energy barriers. In the region between the barriers the potential energy of the electron is zero. The normalized wave function of the electron in the region between the walls is ψ(x) = Asin(bx), where A=0.5nm1/2 and b=1.18nm-1. What is the probability to find the electron between x = 0.99nm and x = 1.01nm.An electron is confined between two perfectly reflecting walls separated by the distance 12 x 10-11m. Use the Heisenberg uncertainty relation to estimate the lowest energy that the particle can have (in eV).
- Which of the following is/are correct for the equation y(x) dx defined for a particle whose state function is y(x) (11) (iii) This equation gives the probability of the particle with the range x to X₂. This equation applies to the particle moving in any dimension. This equation defines relation between the state function and the probability with the range x; to x₂- (a) Only (1) (b) (ii) and (iii) (c) (i) and (iii) (d) (i) and (ii)A particle is in a three-dimensional cubical box that has side length L. For the state nX = 3, nY = 2, and nZ = 1, for what planes (in addition to the walls of the box) is the probability distribution function zero?A quantum mechanical particle moving in one dimension between impenetrable barriers has energy levels ϵ,4ϵ,9ϵ,...ϵ, 4ϵ, 9ϵ, ... , that is En=ϵn2En=ϵ n2 . Suppose that ϵ=0.035eVϵ =0.035 eV for a certain such quantum system. What is the probability (as a percent) that such a system will be in its ground state when it is in contact with a reservoir at room temperature? The probability that the system will be in its ground state when it is in contact with a reservoir at room temperature is
- A particle is in the ground state of an inifite square well with walls at x = 0 and x = a. Suddenly the right wall moves from x = a to x = 2a. If the energy of the particle is measured after the wall expansion, what will be the most probable value of the probability of getting this resultAn electron is in an infinite potential well of width 364 pm, and is in the normalised superposition state Ψ=cos(θ) ψ5-sin(θ) i ψ8. If the value of θ is -1.03 radians, what is the expectation value of energy, in eV, of the electron?