EEE 352 TEST 2 QUESTIONS ANSWERED CORRECTLY LATEST UPDATE 2026

EEE 352 TEST 2 QUESTIONS ANSWERED CORRECTLY LATEST UPDATE 2026 When is Ψ(x) continuous? - Answers Always When is Ψ'(x) continuous? - Answers Wherever the potential is finite When is it possible to separate the time-dependent Schrödinger equation into equations for ψ(x) and φ(t)? - Answers When the potential U(x,t) =U(x), i.e., the potential is static (independent of time). Probability that particle will be reflected. - Answers Reflection Coefficient (R) Probability that particle will be moving past barriers (transmitted). - Answers Transmission Coefficient (T) What is the probability density current of an evanescent wave? - Answers Zero (for a single evanescent wave in a region) When is the allowed energy spectrum of an electron continuous? - Answers Whenever the wave function is delocalized (barrier problems). When is the wave function delocalized? - Answers EU in either of the semi-infinite end regions When is the allowed energy spectrum of an electron discrete? - Answers Whenever the wave function is localized When is the wave function localized? - Answers EU in BOTH end regions. Is the wave function Ψ(x) = A exp -(x/σ)^2 localized? Why or why not? - Answers Yes. It decays (goes to zero) at both positive and negative infinity. What is the group velocity of a standing wave? - Answers Zero When a particle is transmitted THROUGH (not over) a barrier of finite width, in which the particle could not exist classically because EU. It is a purely quantum mechanical effect. - Answers Tunneling How many spatial quantum numbers are there in most three-dimensional problems? - Answers Five (three associated with the motion in space and two associated with spin) Which quantum number(s) determine the energy of an electron in a H atom? - Answers n (determines the energy in any one-electron atom) Which quantum number(s) determine the energy of an electron in a complicated atom? - Answers Both n and l Do particles with spin 2 obey the Pauli exclusion principle? - Answers No (they are bosons) Integer spin - Answers Bosons Do particles with spin 5/2 obey the Pauli exclusion principle? - Answers Yes (they are fermions) Half-integer spin - Answers Fermions Bosons obey... - Answers Bose-Einstein statistics Fermions obey... - Answers Fermi-Dirac statistics Describe the assumed form of the potential energy inside a crystal in the quantized free electron model. - Answers It is constant (zero forces) The thermodynamic work required to add one electron to the body. - Answers Fermi level Should electrons scatter from ion cores in a crystal in the free electron gas model? - Answers Yes (that is a basic assumption of the model) Do electrons scatter from ion cores in a crystal in the free electron gas model experimentally? - Answers No (in reality, electrons are not scattered by a perfectly periodic potential. This is why mean free paths can sometimes greatly exceed the atomic spacing in highly perfect crystals at low temperature. They are only scattered by defects and lattice vibrations (when the potential becomes nonperiodic). This fact is predicted by the energy band model.) How does the shape of f_FD(E) change with temperature? - Answers It "spreads out" near the Fermi level Is E_F strongly dependent on temperature in a metal? - Answers No (It decreases only slightly as T increases (e.g., by about 0.01% from 0 to 300 K)) Spherical surface in both k-space and v_g-space that separates states (inside it) with energies E E_F, which are mostly full, from states (outside it) with energy E E_F, which are mostly empty. - Answers Fermi sphere What happens to a Fermi sphere when an electric field is applied in the -x direction in a real metal? - Answers It will shift in the +x-direction by a finite amount, due to scattering Can positive Hall coefficients be explained by free electron gas models? - Answers No (In these models, the conduction is assumed to be due to negatively-charged electrons, so the Hall coefficients would have to be negative.) Constructive interference of wave reflected from successive planes of atoms. - Answers Bragg reflection In a periodic one-dimensional potential of period a, do we get a new solution of Schrödinger's equation by increasing k_x by (2π/a)? - Answers No (Doing so moves you from one Brillouin zone to the next one, and the same solutions are represented an infinite number of times, once in each Brillouin zone in the repeated-zone representation.) In the quantized free electron model, the Fermi level is mainly determined by the... - Answers Free electron concentration If electrons had spin s = 3/2, but all other laws of nature were unchanged, a 4f orbital in a H atom would be able to hold... - Answers 28 electrons The classical transmission coefficient for a particle with a certain energy meeting a certain potential barrier is one. Therefore,the quantum mechanical transmission coefficient for a particle with the same energy meeting the same barrier... - Answers Is probably something between zero and one The quantized free electron model is most useful for explaining... - Answers The specific heat capacity of the electrons in metals The probability density function of a Bloch electron is... - Answers Spatially periodic with the period of the crystal lattice and independent of time