Draw a picture of the following (unnormalized) wavefunctions for a particle in a 1-D box: + = ₁ + 3 and - = 9₁-93
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A: (a)
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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. %3DGiven a Gaussian wave function: Y(x) = (1/a)-1/4e-ax²/2 Where a is a positive constant 1) Find the normalization (if the wave function is not normalized) 2) Determine the mean value of the position x of the particle : x 3) Determine the mean value of x? : x? 4) Determine the value of Ax = /(x²) – (x)²A quantum mechanical particle of mass m moves in a 1D potential where a) Estimate the ground state energy of the particle. b) Sketch the wave function to the best of your ability.
- An electron moving in a box of length ‘a’. If Z1 is the wave function at x1 = a/4 with n=1 and Z2 at x = a/4 for n=2 find Z1/Z2QUESTION 7 Use the Schrödinger equation to calculate the energy of a 1-dimensional particle-in-a-box system in which the normalized wave function is 4' = e sin(6x). The box boundaries are at x=0 and x=r/3. The potential energy is zero when 0 < x <- and o outside of these boundaries. 18h? m h2 8m h2 36n2m none are correcta 4. 00, -Vo, V(z) = 16a 0, Use the WKB approximation to determine the minimum value that V must have in order for this potential to allow for a bound state.