Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 35, Problem 3P
To determine
The proof that
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Solving the Schrödinger equation for a particle of energy E 0
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Solve the Schrödinger equation for the potential V(x) = |x| and find the eigen values.
Consider the Schrodinger equation for a one-dimensional linear harmonic oscillator:
-(hbar2/2m) * d2ψ/dx2 + (kx2/2)*ψ(x) = Eψ(x)
Substitute the wavefunction ψ(x) = e-(x^2)/(ξ^2) and find ξ and E required to satisfy the Schrodinger equation. [Hint: First calculate the second derivative of ψ(x), then substitute ψ(x) and ψ′′(x). After this substitution, there will be an overall factor of e-(x^2)/(ξ^2) on both sides of the equation which canbe an canceled out. Then, gather all terms which depend on x into one coefficient multiplying x2. This coefficient must be zero because the equation must be satisfied for any x, and equating it with zero yields the expression for ξ. Finally, the remaining x-independent part of the equation determines the eigenvalue for energy E associated with this solution.]
Chapter 35 Solutions
Physics for Scientists and Engineers
Ch. 35 - Prob. 1PCh. 35 - Prob. 2PCh. 35 - Prob. 3PCh. 35 - Prob. 4PCh. 35 - Prob. 5PCh. 35 - Prob. 6PCh. 35 - Prob. 7PCh. 35 - Prob. 8PCh. 35 - Prob. 9PCh. 35 - Prob. 10P
Ch. 35 - Prob. 11PCh. 35 - Prob. 12PCh. 35 - Prob. 13PCh. 35 - Prob. 14PCh. 35 - Prob. 15PCh. 35 - Prob. 16PCh. 35 - Prob. 17PCh. 35 - Prob. 18PCh. 35 - Prob. 19PCh. 35 - Prob. 20PCh. 35 - Prob. 21PCh. 35 - Prob. 22PCh. 35 - Prob. 23PCh. 35 - Prob. 24PCh. 35 - Prob. 25PCh. 35 - Prob. 26PCh. 35 - Prob. 27PCh. 35 - Prob. 28PCh. 35 - Prob. 29PCh. 35 - Prob. 30PCh. 35 - Prob. 31PCh. 35 - Prob. 32PCh. 35 - Prob. 33PCh. 35 - Prob. 34PCh. 35 - Prob. 35PCh. 35 - Prob. 36PCh. 35 - Prob. 37PCh. 35 - Prob. 38P
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