In the ground state of the harmonic oscillator, what is the probability (correct to three significant digits) of finding the particle outside the classically allowed region? (Hint: what are the minimum and maximum values of the coordinates of the respective classical oscillator with a given energy E?) Look in math tables under "Normal distribution" or "Error function" for the numerical value of the integral.

Solution Preview

Hello and thank you for posting your question to Brainmass!

The solution is attached below in two files. the ...

Solution Summary

This solution determines the maximum and minimum values of the coordinates in the classical oscillator using energy, frequency, amplitude, wave function and hence the probability of the particle outside the classically allowed region. All steps are shown with brief explanations for further understanding.

... Calculate the expectation values < x >, < p >, < x^2 > and < p^2 > for the ground state, | 0 >, and the first excited state, | 1 >, of the harmonic oscillator. ...

... The energy levels of a harmonic oscillator are given by: ... N^p different states for the N oscillator system with energy of p h-bar omega above the ground state. ...

...ground and first excited states of this two-fermion system. Express the eigenstates corresponding to these two energy levels in terms of harmonic oscillator...

... well as unperturbed system and some form of harmonic oscillator as perturbation and vice versa, when we have ground state of harmonic oscillator as unperturbed ...

For simple harmonic oscillator H = p^2/(2m) + (K/2)x^2 turn on the potential V(x) = cx^4 Calculate the first order correction to the ground state energy. ...

Compute the uncertainty product for a harmonic oscillator. See attached file. ... can be computed as follows. You start with the ground state wavefunction. ...

Consider a 3-dimensional, spherically symmetric, isotropic harmonic oscillator with a potential energy of [see the ... 1.24) This is exactly the ground state energy ...

... As for any quantum harmonic oscillator, the energy levels are ½ hf, 3/2 hf, 5/2 hf ... the probability of a water molecule being in its flexing ground state and in ...

...Harmonic oscillator with natural frequency. and with energy levels given by. Thus we have. 3. If the particles are spin-0 bosons, then the ground state of the ...

... A H2 molecule can be approximated by a simple harmonic oscillator having a ... the H2 molecule decays from the third excited state down to the ground state? ...