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Problem - Consider a mass moving in a spherically symmetric potential V(r) = kr, k > 0. Suppose you guess that the ground state (l=0) has a radial wave function, R1,0 = √(1/2a3)e-(r/2a)
1) Let amin be the value of the constant a that minimizes the expectation of Hamiltonian. Find an expression for amin in terms of h, k and m. Use 0∫infinity ze-z dz = 1.
2) Explain physically why amin decreases as k increases.
3) This guess for the found state wave function does not fall off fast enough as r goes to infinity. What is the correct asymptotic behavior for very large r?
Compute the probability that more than 1200 units are ordered in one week.
Use this result to find the convolution of h(t) with x(t) where h(t)= e-2t u(t) and x(t) as Wore below, by fire performing the convolution h(t)*u(t) and then cenvolving this with x'(t).
A company's free cash flow was just FCF0= $1.50 million. The weighted average cost of capital is WACC = 10.1%, and the constant growth rate is g = 4.0%. What is the current value of operations?
Discuss Kendra's errors in interpreting the tax laws, and explain the difference between itemized deductions and the standard deduction.
Julia may lease a warming oven for $600 for a six game football home-season game. the oven has 16 shelves, and each shelf is 3 feet by 4 feet. she plans to fill the oven with the food times (pizza, hot dogs and barbecue sandwiches) before the ga..
Draw a tree diagram to illustrate the different possibilities. In hoe many ways will the 2nd , 3rd, and 4th coins all turn heads.
Justify your answer by commenting on the influence of a and l
A cantilever beam, having an extended length L, is subjected to a vertical force F. Assuming that the wall resists this load with linearly varying distributed loads over the length a of the beam portion inside the wall, determine the intensities w..
The firm wants to know how many pounds of wieners of each type to produce to maximize profits. a. Formulate a linear programming model and solve the model by using a computer.
What must the height h of the tent be, and why? Use your answer to derive a piecewise-linear function defining the probability density function p(x) for the domain x ∈ [0, 1]. Derive a piecewise quadratic cumulative distribution function cdf(x) for..
The task is to develop a robot-controlled motorcycle for operation on the moon. Develop a feedback controller to operate the motorcycle on the moon using a feedback controller structure of your choosing. What realistic disturbances would the motorc..
Determine by a projection the point on the hyperplane and determine a vector equation of the line of intersection of the planes
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