Chapter4problem: Difference between revisions
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MarkLingle (talk | contribs) (New page: (Problem submitted by team 9, based on problem 7.11 of Griffiths) (a) Using the wave function <math> \psi= \begin{cases} A*cos(\frac{\pi*x}{a}) & \frac{-a}{2}<x<\frac{a}{2} \\ 0 & oth...) |
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(Problem submitted by team 9, based on problem 7.11 of Griffiths) | (Problem submitted by team 9, based on problem 7.11 of Griffiths) | ||
(a) Using the wave function | '''(a)''' Using the wave function | ||
<math> \psi= | <math> \psi= | ||
\begin{cases} | \begin{cases} | ||
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obtain a bound on the ground state energy of the one-dimensional harmonic oscillator. Compare <math> <H>_{min} </math> with the exact energy. Note: This trial wave function has a discontinuous derivative at <math> \frac{\pm a}{2}</math>. | obtain a bound on the ground state energy of the one-dimensional harmonic oscillator. Compare <math> <H>_{min} </math> with the exact energy. Note: This trial wave function has a discontinuous derivative at <math> \frac{\pm a}{2}</math>. | ||
(b) Use <math> \Psi = B*sin(\frac{\pi*x}{a}) </math> on the interval (-a,a) to obtain a bound on the first excited state. Compare to the exact answer. | '''(b)''' Use <math> \Psi = B*sin(\frac{\pi*x}{a}) </math> on the interval (-a,a) to obtain a bound on the first excited state. Compare to the exact answer. | ||
Revision as of 21:09, 15 April 2010
(Problem submitted by team 9, based on problem 7.11 of Griffiths)
(a) Using the wave function
obtain a bound on the ground state energy of the one-dimensional harmonic oscillator. Compare with the exact energy. Note: This trial wave function has a discontinuous derivative at .
(b) Use on the interval (-a,a) to obtain a bound on the first excited state. Compare to the exact answer.
