Consider an harmonic oscillator with spring constant k and mass m. - Find the cl

Question

Consider an harmonic oscillator with spring constant k and mass m.
- Find the classical frequency of this oscillator as a function of the spring constant and m.

In quantum mechanics, the spectrum of possible energies for this oscillator is given by: En = hf (n + 1/2) where n is a natural number: n = 0, 1, 2, 3, ..., h is Planck’s constant and f is the frequency.
- Find the ground state energy as a function of the spring constant and the mass.
- What is the difference of energy between the second excited state and the ground state?
- Assume now that the oscillator carries a unit of charge, what is the wavelength of the photon emitted as a function of k and m when the oscillator goes from the first excited state down to the ground state?
- What is the wavelength of the emitted photon of the previous question if k = 10eV/ °A2, where °A denotes Angstrom and eV: electron volt. Is the emitted photon in the visible spectrum of a human eye?

thank you so much for any help!

Explanation / Answer

Force   F =   -kx m ( d2x / dt2 )   = -kx   ==> ( d2x / dt2 )   = -( k/m) x comparing this simple harmonic equation , we get   ( d2x / dt2 )   = - 2 x       2    =  k/m      == >   frequency f = (1/2 ) sqrt (   k/m  ) ------------------------------------- En   = hf ( n + (1/2))   for ground state energy n =    0 E0    =   (1/2)hf   =   (h / 4 ) sqrt (   k/m  ) ------------------------------------- second exited state energy   n = 2    E2    =   ( 5/2) hf   energy difference   E = E2   - E0    =   2hf   =   ( h / ) sqrt (   k/m  ) ---------------------------------------------- when an unit positive charge is added the energy levels undergo perturbation effect hence   the energy levels shifted   by   electrostatic potential energy -qkx i hope this will   helps u i hope this will   helps u

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.