Numerically solve the time-independent Schrödinger equation for the one-dimensional quantum harmonic oscillator potential like we did in lecture but for the first excited state (which is odd, so choose the appropriate boundary conditions). Use the first- order forward Euler method with a stepsize h = 0.01 and find the dimensionless energy eigenvalue e to at least eight significant figures. Use any programming language that you wish. Plot the wavefunction, f(u) which is a proxy for (x).
Numerically solve the time-independent Schrödinger equation for the one-dimensional quantum harmonic oscillator potential like we did in lecture but for the first excited state (which is odd, so choose the appropriate boundary conditions). Use the first- order forward Euler method with a stepsize h = 0.01 and find the dimensionless energy eigenvalue e to at least eight significant figures. Use any programming language that you wish. Plot the wavefunction, f(u) which is a proxy for (x).
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Two dimensional motion with air drag (think golf ball trajectory) is not integrable, but purely horizontal motion and purely vertical motion are separately integrable.
Transcribed Image Text:Numerically solve the time-independent Schrödinger equation for the one-dimensional
quantum harmonic oscillator potential like we did in lecture but for the first excited
state (which is odd, so choose the appropriate boundary conditions). Use the first-
order forward Euler method with a stepsize h = 0.01 and find the dimensionless energy
eigenvalue e to at least eight significant figures. Use any programming language that
you wish. Plot the wavefunction, f(u) which is a proxy for (x).
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