Given: phi(x,y) satisfies Laplace’s Equation, show that Psi(x,y)=(x^2+y^2)*phi(x,y) satisfies the biharmonic equation. x,y) Setisfics satisfies the...
The Schrodinger equation for a particle in a ring can be expressed as H cap psi(phi) = E psi(phi), where H cap = -h^2 partial^2/21 partial phi^2; psi(phi) = 1/squareroot 2 pi e^-ik phi, k is an integer What is the potential energy? What is the kinetic energy? Write the Schrodinger equation Derive the eigenvalue Show that psi(phi) = psi(phi + 2 pi) Derive an expression for the probability density for a particle in a ring?
The question is 1.3 but the Psi(x,0) and phi(k) are given in the
previous two parts
1.1 Consider a free particle in one-dimension with a wavefunction at t-0 Show that Ψ is normalized. 1.2 Show that the momentum wavefunction is Notice that lin (k-ak-k) 1.3 we can find Ψ(r) at any time t by: (ie. Ψ(x,t) is given by the Schrodinger' egn and the initial condition Ψ(x Show that iht 2mA イAr /2 2mA
Show that the function y = cos (ln(x)] satisfies the differential equation 22 day dy +2 dx +y = 0. dc2
First, verify that y(x) satisfies the given differential equation. Then, determine a value of the constant C so that y(x) satisfies the given initial condition. Use a computer or graphing calculator to sketch several typical solutions of the given differential equation, and highlight the one that satisfies the given initial condition. y' =y+3; y(x) = CeX-3; y(0) = 8 What step should you take to verify that the function is a solution to the given differential equation? O A. Differentiate...
Find the solution of the differential equation that satisfies the given initial condition. y' tan(x) = 7a + y, y(Tt/3) = 7a, 0 < x < 7/2, where a is a constant. 4. V3 X
Find the solution of the differential equation that satisfies the given initial condition. y' tan(x) = 7e + y, y(7/3) = 7a, 0 < x < 77/2, where a is a constant. 4 V3 X
(a) Show that, if y satisfies the Euler-Lagrange equation associated with the integral 2. qy2) dx, I = (6) where p() and q(x) are known functions, then I has the value 12 (b) Show that, if y satisfies the Euler-Lagrange equation associated with (6) and if z(x) is an arbitrary differentiable function for which z(x)z(r2) = 0, (7) 1 then (yyz)da= 0. + Hence show that by replacing y in (6) by the function (y + z), where the condition...
Show that a function w(x, y) = cos(2x + 2ct) satisfies wave equation.
stress analysis please answer ASAP
Show that Airy's stress function D = Cre sine satisfies the biharmonic equation. Also determine the stresses in polar co-ordinate system. 2 A 10-in. length of steel tubing (with properties of E 30 X 106 psi, v = 0.3 and a 7X10-5 F) having a cross-sectional area of 1 square in is installed with fixed ends so that it is stress- free at 80°F measurements indicate that the fixed ends separate by 0.008 in. What...
Suppose f is a function that satisfies the equation f (x + y) = f (x) + f(y) + xºy + xy2 + xyz + xy for all real numbers x and y. Suppose also that f(x) lim = -1. Find f' (a). Show your work in 30 the PDF version of the test. 2