An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter A.3, Problem 14P
To determine
To Draw:An energy level diagram for a nonrelativisticparticle confined inside a three-dimensional cube-shaped box and all states with energies below
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Determine the heat capacity of a two-dimensional layer of atoms in the Debye model. As in the lecture, start with the
calculation of the phonon density of states in 2D and solve the integral for the inner energy thereafter. Demonstrate
that the heat capacity in 2D scales with T?. You may use the following approximation: J
x2
-dx = 2.404.
ex-1
In the following questions, we will use quantum states made up of the hydrogen energy
eigenstates:
Q1: Consider the election in a hydrogen atom to initially be in the state:
F
A.
B.
C.
a) What is the probability of measuring the energy of this state and obtaining E₂?
√3
√
vnim (r0,0)=R(r)Y," (0,0)
always
Y(t = 0) = √3 R₁OYO
at t=0 but something different at t>0
²
at t=0 but something different at t>0
D. always
3
+
E. Something else.
b) Explain your answer.
R₂₁ + R32Y₂¹
Consider the following wave function.
TT X
a
= B sin(-
(x) = E
2 π.χ.
a
−) + C · sin(²
a. Does this function describes a particle-in-a-box acceptable wave function? Name
the conditions to be fulfilled.
b. Is this function an eigenfunction of the total energy operator H when H is the
Hamilton operator.
Chapter A Solutions
An Introduction to Thermal Physics
Knowledge Booster
Similar questions
- Starting from the N(p) expression of a 3D conductor, derive an expression for the exact density of states D(E) for the 3D conductor in the below graph (You have to show all the steps that lead to your final answer). The length of the conductor is given as L = 20 nm and the diameter is given as D= 4 nm. The +E.. 2mo energy momentum relationship is given as: E =arrow_forwardSuppose you have 2 russet potatoes in your pantry that could be in any one of four states ranging from fresh to um...not so fresh...let's quantify these states in terms of energies: 0 eV (fresh), 1 eV, 2 eV, 3 eV (nope). Compute the probability of each potato being in the ground state and the first state, respectively, at а. а сool 290 K. b. Assuming the potatoes will survive, how does the probability change at a temperature 5x greater? What is the average energy of the potato situation for these two temperatures? С.arrow_forwardAre all energy levels equally spaced with respect to n? If not, do they become more or less closely spaced as n increases? Draw a new figure of 4 horizontal lines where each horizontal line corresponds to one energy level. Place the horizontal lines vertically to scale such that they are spaced accurately according to their energy, and label your lines corresponding to n=1, n=2, etc. Using this diagram, identify the largest energy transition between two adjacent energy levels. Calculate this energy difference and the corresponding frequency and wavelength of the emitted photon. Identify the largest energy transition that can occur between any two levels in your diagram. Calculate the energy for this transition along with the corresponding wavelength of the emitted photon.arrow_forward
- Consider an electron trapped in a 20 Å long box whose wavefunction is given by the following linear combination of the particle's n= 2 and n = 3 states: .= ((x,tvי 2nx sin V10 ´3x - sin 4 where E, a 2ma² a. Determine if this wavefunction is properly normalized. If not, determine an appropriate value for a normalization constant. b. Show that this is not an eigenfunction to the PitB problem. What are the possible results that could be returned when the energy is measured and what are the probabilities of measuring each of these results? c. Calculate Y(x,1) = ¥° (x,1)¥ (x.1) and sketch what this looks like for t=0, 3th 2xh ,and 1 (E,-E,) You will likely want 2(E,- E.) (E,-E.)' to use a graphing program such as Excel, Mathematica, or Matlab for this. What happens to the most likely position to find the particle as time progresses? Does it move? If so, with what frequency does it move? 2(E, – E,)'arrow_forwardConsider a particle in a one-dimensional rigid box of length a. Recall that a rigid box has U (x) = 00 for x a, and U () = 0 for 0 )arrow_forwardA particle in one dimension (-∞ 0). a. Is the energy spectrum continuous or discrete? Write down an approximate expression for the energy eigenfunction specified by E. Also sketch it crudely. b. Discuss briefly what changes are needed if Vis replaced by V = λ | x |.arrow_forward
- Calculate: a. The mean of the displacement of the oscillator from equilibrium when a harmonic oscillator is in the v=0 and v=1 quantum states? Explain the origin of similarity and differences. b. The mean of the square of the displacement when a harmonic oscillator is in the v=0 and v=1 quantum states? Explain the origin of similarity and differences. 6.arrow_forwardA conduction electron is confined to a metal wire of length (1.46x10^1) cm. By treating the conduction electron as a particle confined to a one-dimensional box of the same length, find the energy spacing between the ground state and the first excited state. Give your answer in eV. Note: Your answer is assumed to be reduced to the highest power possible. Your Answer: x10 Answerarrow_forward1) Consider a system consisting of two particles, each of which can occupy any one of three single-particle states, with energy 0, e and 2e. a) How many states are there if the particles are bosons? Write down the partition function for this system? b) function for this system? How many states are there if the particles are fermions? Write down the partitionarrow_forward
- Consider an electron trapped in a 20 Å long box whose wavefunction is given by the following linear combination of the particle's n = 2 and n = 3 states: ¥(x,t) =, 2nx - sin ´37x - sin 4 where E, 2ma² a a. Determine if this wavefunction is properly normalized. If not, determine an appropriate value for a normalization constant. b. Show that this is not an eigenfunction to the PitB problem. What are the possible results that could be returned when the energy is measured and what are the probabilities of measuring each of these results?arrow_forwardI1 This time, let us consider a maxed spin state in which the electrons have equal probabilities of being in the pure states 8x+) and sy+)..arrow_forwardConsider a particle of spin 1/2 whose normalized quantum state is given by l6) = V 2.1.0, +) + / 2.1,1.-). |2, 1,0, +) + Calculate the expectation values as well as the corresponding probability if measured d)§., e) j², f).İ2.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax