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Consider a particle in a box with infinitely high walls and zero potential between x=0 and x=L. Now consider a trial wave function, y(x) = Nx(L − x). a. Sketch this wave function. b. Find the normalization factor, N. C. Estimate the energy of this system. d. Compare your result with the exact ground state energy of this system.

Consider a particle in a box with infinitely high walls and zero potential between x=0 and x=L. Now consider a trial wave function, y(x) = Nx(L − x). a. Sketch this wave function. b. Find the normalization factor, N. C. Estimate the energy of this system. d. Compare your result with the exact ground state energy of this system.

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Consider a particle in a box with infinitely high walls and zero potential between x=0 and x=L. Now consider a trial wave function, \( \psi(x) = Nx(L-x) \). a. Sketch this wave function. b. Find the normalization factor, N. c. Estimate the energy of this system. d. Compare your result with the exact ground state energy of this system.
Transcribed Image Text:Consider a particle in a box with infinitely high walls and zero potential between x=0 and x=L. Now consider a trial wave function, \( \psi(x) = Nx(L-x) \). a. Sketch this wave function. b. Find the normalization factor, N. c. Estimate the energy of this system. d. Compare your result with the exact ground state energy of this system.
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