1. The wavelength spectrum of the radiation energy emitted from a system in thermal equilibrium is observes to have a maximum value which decreases with increasing temperature. Outline briefly the significance of this observation for quantum physics.
2. The “stopping potential” in a photoelectric cell depends only on the frequency v of the incident electromagnetic radiation and not on its intensity. Explain how the assumption that each photoelectron is emitted following the absorption of a single quantum of energy hv is consistent with this observation.
3. Write down the de Broglie equations relating the momentum and energy of free particle to, respectively, the wave number k and angular frequency w of the wave-function which describes the particle.
4. Write down the Heisenberg uncertainty Principle as it applies to the position x and momentum p of a particle moving in one dimension.
5. Estimate the minimum range of the momentum of a quark confined inside a proton size 10 ^ -15 m.
6. Explain briefly how the concept of wave-particle duality and the introduction of a wave packet for a particle satisfies the Uncertainty Principle.

# problems in Quantum Mechanics. 1. show that the commutator obeys: [A,B] = -[B,A] [A,B+C]=[A,B] + [A,C] [A,BC]=[A,B]C+B[A,C] [A,[B,C]]+[B,[C,A]]+[C,[A,B]]= ...

One dimensional Quantum Mechanics problems. 1, Show that for any normalized |u> , the inequality E0 <= <u|H|u> holds, where E0 is teh lowest energy eigenvalue. ...

... one for n=1 and one for n=2. This is a problem dealing with a mixed system where two dimensions are governed by quantum mechanics and the third by classical. ...

... But, beyond the problem of gravity, Newton's work was also important in establishing ... equation), he began what we now refer to as quantum physics which brought ...

... position today (take for instance the shift of authority from linear to quantum physics). ... that is looked to explain and solve scientific problems and challenges ...