Thursday, August 22, 2019
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, |È10|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 ‘š ð Å"â€Ã¢â€ž (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 ‘ ¢ = √ð › ¼Ã° ‘ ¥ 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 É)? 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  ± imÉx) A=- â„ ^2 d^2/ 2mr^2d (b) Plot È10 and |È10|2(use u rather than x for your independent variable); your |È10|2 plot should look like Figure 6.11. (c) Normalize È10 (use u); Normalization the stationary wave functions are r a 1 2 2 Èn (x) = 2n√À 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 › ¼Ã° ‘ ¥ ≠¤ 0.5. Use 3 significant figures for these numerical answers. (e) What is âÅ' ©Ã° › ¼Ã° ‘ ¥2âÅ' ª for this excited state?
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment