{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

486_HW5 - Physics 486 FA07 Homework Set 5 Due Oct 4 2007 1...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 486 FA07 Homework Set 5 Due: Oct 4, 2007 1) Based on Griffiths 2.22 . A free particle has the initial Gaussian wave function Ψ (x,0) = A e -ax ² , where A and a are constants (a is real and positive). (a) Determine the constant A. (b) Find the time-dependent wavefunction Ψ (x,t). Hint: Integrals of the function e - (ax ² +bx) (limits - to + ) can be performed by “completing the square”: Let y = a (x+(b/2a)) and note that ax ² +bx = y ² - (b ² /4a). (c) Find | Ψ (x,t)| ² . Express your answer in terms of the quantity w = [a/(1+(2at /m) ² )] 1/2 . Sketch | Ψ (x,t)| ² as a function of x at t = 0, and once again at some very large time t. Qualitatively, what happens to | Ψ | ² as time goes on? 2) Double well potential. Consider the “double square well” potential model of an H 2 or NH 3 molecule. Suppose the depth, V 0 , and the width, a , are fixed and large enough that several bound states occur. The separation, b , can be varied. (a) Sketch the ground state wave function, ψ 1 , and the first excited state, ψ 2 , for the following cases: (i) b=0; (ii) b a; and (iii) b >>a.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}