The Quantum Harmonic Oscillator

Vibrations of the hydrogen molecule \(\mathrm{H}_{2}\) can be modeled as a simple harmonic oscillator with the spring constant \(k=1.13 \times 10^{3} \mathrm{~N} / \mathrm{m}\) and mass \(m=1.67 \times 10^{-27} \mathrm{~kg}\). (a) What is the vibrational frequency of this molecule? (b) What are the energy and the wavelength of the emitted photon when the molecule makes transition between its third and second excited states?

Text Transcription:

H_2

k=1.13 times 10^3 N/m

m=1.67 times 10^-27 kg

Lecture 7 Potential from a distribution of charges X V = 1 qi 4⇡✏0 ri §Smooth distribution 1 X qi 1 Z ⇢ V = = dV 4⇡✏0 i ri 4⇡✏ 0 r § of point charges is usually much simpler thanup calculating the electric field •It’s a scalar Electric Potential from Two Oppositely Charged Point Charges §The electric field lines from two oppositely charge point charges are a little more complicated §The electric field lines originate on the positive charge and terminate on the negative charge §The equipotential lines are always perpendicular to the electric field lines §The red lines represent positive electric potential §The blue lines represent negative electric potential §Close to each charge, the equipotential lines resemble those from a point charge 22 Electric Potential from Two Identical Point Charges §The electric field lines from two identical point charges are also complicated §The electric field lines originate on the positive charge and terminate at infinity § Again, the equipotential lines are always perpendicular to the electric field lines §There are only positive potentials §Close to each charge, the equipotential lines resemble those from a point charge 23 Example: Superposition of Electric