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A particle in the ground state of the quantum harmonic oscillator, which is described by the following wavefunction for all values of x :  wave function found in image  1.Determine the energy of this particle, and show that its wavefunction satisfies the appropriate time-dependent Schro ̈dinger equation. 2.Determine the maximum displacement from x = 0 that a classical particle with the same en- ergy is allowed to have in this potential. Finally, write down an expression (without evaluating the integral) for the probability of finding the quantum particle outside of the classically allowed region.

A particle in the ground state of the quantum harmonic oscillator, which is described by the following wavefunction for all values of x :  wave function found in image  1.Determine the energy of this particle, and show that its wavefunction satisfies the appropriate time-dependent Schro ̈dinger equation. 2.Determine the maximum displacement from x = 0 that a classical particle with the same en- ergy is allowed to have in this potential. Finally, write down an expression (without evaluating the integral) for the probability of finding the quantum particle outside of the classically allowed region.

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A particle in the ground state of the quantum harmonic oscillator, which is described by the following wavefunction for all values of x :  wave function found in image 

1.Determine the energy of this particle, and show that its wavefunction satisfies the appropriate time-dependent Schro ̈dinger equation.

2.Determine the maximum displacement from x = 0 that a classical particle with the same en- ergy is allowed to have in this potential. Finally, write down an expression (without evaluating the integral) for the probability of finding the quantum particle outside of the classically allowed region.

Y(t, x) = (²) * exp{-1 az²} exp{-1 wt}, where a = mw/h, and where m and w are constants. The potential for this system is given by V = 1/mw²x².
Transcribed Image Text:Y(t, x) = (²) * exp{-1 az²} exp{-1 wt}, where a = mw/h, and where m and w are constants. The potential for this system is given by V = 1/mw²x².
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