(8) Suppose y(y) = A Sin By, and y(y) = B Cos By are each solution...
HNTV 8) Suppose v(y) = A Sin By, and y(y)=B Cos By are each solution to the particle in the box problem with the Hamiltonian, H = -(h/8x ma?)d/dy. Show that the linear combination (y) - A Sin By - B Cos By is also a solution and then determine the eigenvalue. (Hint: Hv=Ev). The Synthesis of 1,3,5,7,9,11,13-tetradecaheptaene conjugated compound with the formula H-[CH=CH]7-H produced a trace amount as reported by (Alexander Mebane, JACS 74 (20), page 5227-5229 (1952). The...
8) Suppose (x) - Ce, and (x) - Deare cach solution to the particle in the box problem with the Hamiltonian, H- (-/8"ma)d/dx.Show that the linear combination (x) -C +De is also a solution. Determine the cigenvalue? (Hint: Hy-Ev).
8) Suppose (x) - Ce, and (x) - Deare cach solution to the particle in the box problem with the Hamiltonian, H- (-/8"ma)d/dx.Show that the linear combination (x) -C +De is also a solution. Determine the cigenvalue? (Hint: Hy-Ev).
8) Suppose (x) - Ce, and (x) - Deare cach solution to the particle in the box problem with the Hamiltonian, H- (-/8"ma)d/dx.Show that the linear combination (x) -C +De is also a solution. Determine the cigenvalue? (Hint: Hy-Ev).
solu 4. The principle of superposition (in quantum mechanics) states that if two or more Solutions are each solution to the Schrodinger cquation, then their linear combinations are also solution to the Schrodinger equation. Each of y(x) = A sin ax, V(x) = B cos ax, V(X) Celax, and y(x) =D elox is a solution to the particle in the box problem. Show that linear combinations v(x) = A sin ax + B cos ax and y(x) = Celax +...
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0
4. (a Let (sin( x cos( ) dr...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
1. Identify each of the following equations as linear or nonlinear and also determine their order dy (a) y = t 3 3 (b) ( dy + (c) sin t (d) (1y) sin t ( cos2 t 1 y sin(t)= 0 (e) Int +3etdy dt (f) 2y'-y2 =e (g) y"(t2 1)y+cos(t (h) y"sin(ty)y(t21)y 0 = 0
1. Identify each of the following equations as linear or nonlinear and also determine their order dy (a) y = t 3 3 (b)...
2 + COS- 2.ry dy d 1+y2 = y(y + sin x), 7(0) = 1. 3. [2cy cos(x+y) - sin x) dx + x2 cos (+²y) dy = 0. 4. Determine the values of the constants r and s such that (x,y) = x'y is an Integrating Factor for the following DE. (2y + 4x^y)dr + (4.6y +32)dy = 0. 2. C = -1 You need to find the solution in implicit form. 3. y = arcsin (C-cos) 4. r=...
(1 point) Solve the following differential equation: (tan(x) 8 sin(x) sin(y))dx + 8 cos(2) cos(y)dy = 0. = constant. help (formulas)