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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?
What is the difference between retained earnings and net income?
Compute B1 and B0 (for this I am having trouble finding the covariance and Sx if you could please write that out in detail)
1 consider the following lpmaximize z4x15x23x3subject tox1x24x3le6x12x2x3le7x14x22x3le12a add slack variables x4 x5 and
You plan to buy a house in 6 years. You want to save money for a down payment on the house. You are able to put $256/month in a savings account with an annual rate of 6.67% which is compounded monthly. How much money will be in the account when yo..
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Solving the final nonlinear equation in the problem statement for θ. Once θ is known, you can this solve for the location of the football, i.e., solve for x and y using a series (or vector) of time values.
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Construct a program where inputs: the coefficients (a1, a2, a3, a4, a6) of an elliptic curve E : y 2 + a1xy + a3y = x 3 + a2x 2 + a4x + a6 and an integer n. The output Δ (discriminant of E) mod n and the j invariant of E mod n.
A cylinder with initial volume V contains a sample of gas at pressure p. The gas is heated in such a way that its pressure is directly proportional to its volume. After the gas reaches the volume 3V and pressure 3p, it is cooled isobarically to it..
What equation will generate the number of tiles for a height of n? Use the diagrams (you can expand them) and the table to show how you arrived at your equation.
To analyze the winning times for the Olympic Men's 400 Meter Dash using a linear model. The winning times were gathered for the most recent 16 Summer Olympics, post-WWII. (More data was available, back to 1896.)
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