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- 3. For free particles in two dimensions, what is density of states (DOS) in low speed limit (=p²/2m), and in high speed limit (=pc)?200 5 Wave Packets 6 The Heisenberg Uncertainty Principle 11. Approximately what range of frequencies must be superimposed to create this wave packet? 12. A telecommunication system uses pulses with a duration of 5 ns. a. About how many such pulses can be transmitted per second? b. What is the minimum bandwidth needed to transmit these pulses? 13. Wave packets are shown for particles 1, 2, and 3. MA ^^^^^ M. Particle 1 AMA Particle 2 $(1) Which particle can have its velocity known most precisely? Explain. 1 ps Hollo Aff Particle 35. A microscopic oscillator has its first and second excited states 0.05 eV and 0.10 eV above the ground-state energy. Calculate the Boltzmann factor for the ground state, first excited state, and second excited state, at room temperature.
- 4. Use the variational principle to estimate the ground state energy of a particle in the potential (∞0 x < 0 U(x) = \cx x≥0 Take xe-bx as a trial function.6.An atomic hydrogen atom is immersed in a magnetic field of 12.44 T. For the 2p to 1s transition more than one line will appear due to the Zeeman effect. What is the smallest wavelength separation of these lines? (in units of picometers (pm)).