Quantum Oscillator Problem Assignment Example | Topics and Well Written Essays - 250 words

Quantum Oscillator Problem - Assignment Example Figure 6.11 shows a plot of the 10th excited state probability density, |ψ10|2. Mathematica has the Hermite polynomials built-in. The quantum oscillator wave functions are given in equation 6.57; these wave functions are not normalized. The ÃŽ ± in these equations is ð â€˜Å¡ ð Å"”â„ (HW Problem 6.36 and in-class work). The argument of the Hermite polynomials in equation 6.57 is listed as â€Å"x† but you will want to use ð â€˜ ¢ = √ð â€º ¼Ã° â€˜ ¥ as the argument when you are actually write down or program the Hermite polynomials. (a) Write down the (un-normalized) wave function for the 10th excited state; you can write it in terms of ÃŽ ±. Also write down the energy for this state (write this energy in terms â„  and ω)? This type of which energy act on the energy eigenstates of the harmonic oscillator potential producing a un-normalized state of higher or lower energy. a ± =1/√2m(~/i∂/∂x  ± imωx) A=- â„ ^2 d^2/ 2mr^2d (b) Plot ψ10 and |ψ10|2(use u rather than x for your independent variable); your |ψ10|2 plot should look like Figure 6.11. (c) Normalize ψ10 (use u); Normalization the stationary wave functions are r a 1 2 2 ψn (x) = 2n√π n! Hn (ax) e− a x 2 .The diodes are available in the normalized E24  ±1 % (BZX84-A),  ±2 % (BZX84-B) and approximately  ±5 % (BZX84-C) tolerance range. The series includes 37 breakdown voltages with nominal working voltages from 2.4Vto75 V. (d) Find the probability that the electron is in the region −0.5 ≠¤ √ð â€º ¼Ã° â€˜ ¥ ≠¤ 0.5. Use 3 significant figures for these numerical answers. (e) What is âÅ' ©Ã° â€º ¼Ã° â€˜ ¥2âÅ' ª for this excited state?