Show that the energy of a simple harmonic oscillator in the n = 1 state is 3ℏω/2 by substituting the wave function ψ1 = axe-αx2/2 directly into the schroedinger equation, as broken down in the following steps. first, calculate dψ1/dx, using a, x, and α. dψ1/dx = second, calculate d2ψ1/dx2, using a, x, and α. d2ψ1/dx2 = third, calculate α2x2ψ1 - d2ψ1/dx2, using a, x, and α. α2x2ψ1 - d2ψ1/dx2 = fourth, calculate (α2x2ψ1 - d2ψ1/dx2)/ψ1, using a, x, and α. (α2x2ψ1 - d2ψ1/dx2)/ψ1 = finally, calculate e ≡ [(α2x2ψ1 - d2ψ1/dx2)/ψ1]ℏ2/(2m), using a, x, α, m, ω, and ℏ. e ≡

How is acceleration calculated? a. initial velocity - final velocity / timeb. initial velocity + final velocity / timec. final velocity - initial velocity / timed. final velocity / timele select the best answer from the choices provided0oood00save and exitnextmark this and return

Ethanol has a heat of vaporization of 38.56 kj/mol and a normal boiling point of 78.4 c. what is the vapor pressure of ethanol at 14 c?

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?