Determine normalization factor N for the function =Ne-kx describing particle in the region from x=0 to x = + ∞
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Determine normalization factor N for the function =Ne-kx describing particle in the region from x=0 to x = + ∞.
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- Calculate the uncertainties dr = V(x2) and op = V(p²) for %3D a particle confined in the region -a a, r<-a. %3DAt time t = 0 a particle is described by the one-dimensional wave function 1/4 (a,0) = (²ª) e-ikre-ar² where k and a are real positive constants. Verify that the wave function (r, 0) is normalised. Hint: you may find the following standard integral useful: Loze -2² dx = √,A particle with mass m is in the state .2 mx +iat 2h Y(x,t) = Ae where A and a are positive real constants. Calculate the expectation values of (x).
- 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, ....Please asapA 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?