1. ### Fermi temperature of a 1D electron gas

Homework Statement Consider a one-dimensional metal wire with one free electron per atom and an atomic spacing of ##d##. Calculate the Fermi temperature. Homework Equations Energy of a particle in a box of length ##L##: ##E_n = \frac{\pi^2 \hbar^2}{2 m L^2} n^2## 1D density of states...
2. ### Poisson's equation in 1D with point source

Homework Statement Solve ##\Delta\phi = -q\delta(x)## on ##\mathbb{R}##. Correct answer: ##\phi = -\frac{q}{2}|x| + Ax + B## Homework Equations The Attempt at a Solution In one dimension the equation becomes ##\frac{d^2 \phi}{d x^2} = -q\delta(x)##. We integrate from ##-\infty## to ##x## to...
3. ### Probability Density in an infinite 1D square well

Homework Statement The wave function of a particle of mass m confined in an infinite one-dimensional square well of width L = 0.23 nm, is: ψ(x) = (2/L)1/2 sin(3πx/L) for 0 < x < L ψ(x) = 0 everywhere else. The energy of the particle in this state is E = 63.974 eV. 1) What is the rest energy...
4. ### Simple constant acceleration/equation of motion question

Homework Statement A 747 Jumbo Jet must reach a speed of 290km/h by the end of the runway to lift off. The 15L-33R runway at Toronto International Airport is 2,770 meters long. The main Toronto Island Airport runway 08-26 is 1216 meters long. Assuming the jet has a constant acceleration, for...
5. ### Coefficient of restitution in different frames of references

To simplify my question I would like to use a random example (although, the issue holds regardless of the numbers you pick). Suppose two objects collide (head-on) in one dimension. The initial parameters are as follows (units are irrelevant): m1=1;m2=2;u1=3;u2=-4; Also, suppose that exactly...
6. ### Thermal Ckt Parallel Configuration & 1-D HeatFlow Contradictory?

1. My Conceptual Questions (5) is at 3. CONSIDER: Case 1: two dissimilar slabs of material (say slab 1 and slab 2) connected in series (bonded at their interface). There is a temperature difference: T1 @ slab1 and T2 @ slab2. Case 2: two dissimilar slabs of material bonded together, i.e...