Question

Studying through lecture slides for a quiz - can someone explain how we were supposed to know A=? And how we arrived at y= for the integral?

Example: Gaussian wave packet A free particle has the initial wave function. Find Y(x,t). O how to knows Y(x,0) = Ae -ax? A=291942 Here a and A are real and positive. What is A? 1/4 V too A. a Bova c. a D. (29) 1/4 At = 0 $(x) = vzw Sa Pille-ikody explain horny -12 (29)"|-*-**-* >= vas nie die bestany +00 120 1/4 |— 1271 n k2 11 4a = | Tai Chose for e-v2 dy this ye e Va J-00 (2īta)1/4 e 4a

Answer 1

1 First Answer om The normalization condition for any quantum mechanical Ware-function + + tells us , l 4*(x) 4 () dve 3) 1² dx = 1. In our case, 4) - Acax? ; : 1°()2 - A 7-2027 In our case, +00 2 This A dx = 1. è bz2 i place I → A. - 1 here, b=20. 1 As given in slide.

(2) Second Answer in too as NO Whenever you encounter reatika dx kind of integral, you should look for a perfect square form of this integral, i.e, how to make the power of the exponential as a perfect square. This is useful as we already know the formula to e byr A. Thus, I ear ikx de e artike de to -a2"-2/([Tan) iki + Cell

- o - [Eba+ 2.62 +673) Box 21a 1. we substitute ya vaz titana or, dy = ra da Thus, we choose , y. Ta z tiket ik y = The minus sign given in the slide is wrong as you can logically infer from above.