Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 5, Problem 45E
(a)
To determine
To write the conditions of wave function.
(b)
To determine
To tell about the reason why the constants cannot be solved from the boundary conditions.
To determine
To tell about the reason why the constants are not solved physically.
(d)
To determine
To show
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
help with modern physics question
where
and
kyk₂
I
2
k
2m E
2
ħ²
2m
ħ²
(V-E)
3 Show that the solutions for region II
can also be written as
2/₁₂ (²) = Ccas (₁₂²) + D sin (k₂²)
for Z≤ 1W/
4 Since the potential well Vez) is symmetrical,
the possible eigen functions In You will
be symmetrical, so Yn will be either
even or odd.
a) write down the even solution for
region. II
b) write down the odd solution
region
for
on II
In problem 2, explain why A=G=0₁
Consider an infinite well, width L from x=-L/2 to x=+L/2. Now
consider a trial wave-function for this potential, V(x) = 0 inside the well
and infinite outside, that is of the form (z) = Az. Normalize this
wave-function. Find , .
Chapter 5 Solutions
Modern Physics
Ch. 5 - Prob. 1CQCh. 5 - Prob. 2CQCh. 5 - Prob. 3CQCh. 5 - Prob. 4CQCh. 5 - Prob. 5CQCh. 5 - Prob. 6CQCh. 5 - Prob. 7CQCh. 5 - Prob. 8CQCh. 5 - Prob. 9CQCh. 5 - Prob. 10CQ
Ch. 5 - Prob. 11CQCh. 5 - Prob. 12CQCh. 5 - Prob. 13CQCh. 5 - Prob. 14CQCh. 5 - Prob. 15CQCh. 5 - Prob. 16CQCh. 5 - Prob. 17CQCh. 5 - Prob. 18CQCh. 5 - Prob. 19ECh. 5 - Prob. 20ECh. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Prob. 25ECh. 5 - Prob. 26ECh. 5 - Prob. 27ECh. 5 - Prob. 28ECh. 5 - Prob. 29ECh. 5 - Prob. 30ECh. 5 - Prob. 31ECh. 5 - Prob. 32ECh. 5 - Prob. 33ECh. 5 - Prob. 34ECh. 5 - Prob. 35ECh. 5 - Prob. 36ECh. 5 - Prob. 37ECh. 5 - Prob. 38ECh. 5 - Prob. 39ECh. 5 - Prob. 40ECh. 5 - Prob. 41ECh. 5 - Prob. 42ECh. 5 - Obtain expression (5-23) from equation (5-22)....Ch. 5 - Prob. 44ECh. 5 - Prob. 45ECh. 5 - Prob. 46ECh. 5 - Prob. 47ECh. 5 - Prob. 48ECh. 5 - Prob. 49ECh. 5 - Prob. 50ECh. 5 - Prob. 51ECh. 5 - Prob. 52ECh. 5 - Prob. 53ECh. 5 - Prob. 54ECh. 5 - Prob. 55ECh. 5 - Prob. 56ECh. 5 - Prob. 57ECh. 5 - Prob. 58ECh. 5 - Prob. 59ECh. 5 - Prob. 60ECh. 5 - Prob. 61ECh. 5 - Prob. 62ECh. 5 - Prob. 63ECh. 5 - Prob. 64ECh. 5 - Prob. 65ECh. 5 - Prob. 66ECh. 5 - Prob. 67ECh. 5 - Prob. 68ECh. 5 - Prob. 69ECh. 5 - Prob. 70ECh. 5 - Prob. 71ECh. 5 - In a study of heat transfer, we find that for a...Ch. 5 - Prob. 73CECh. 5 - Prob. 74CECh. 5 - Prob. 75CECh. 5 - Prob. 76CECh. 5 - Prob. 77CECh. 5 - Prob. 78CECh. 5 - Prob. 79CECh. 5 - Prob. 80CECh. 5 - Prob. 81CECh. 5 - Prob. 82CECh. 5 - Prob. 83CECh. 5 - Prob. 84CECh. 5 - Prob. 85CECh. 5 - Prob. 86CECh. 5 - Prob. 87CECh. 5 - Prob. 88CECh. 5 - Consider the differential equation...Ch. 5 - Prob. 90CECh. 5 - Prob. 91CECh. 5 - Prob. 92CECh. 5 - Prob. 93CECh. 5 - Prob. 94CECh. 5 - Prob. 95CECh. 5 - Prob. 96CECh. 5 - Prob. 97CECh. 5 - Prob. 98CE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- The odd parity eigenstates of the infinte square well , with potential V = 0 in the range −L/2 ≤ x ≤ L/2, are given by : (see figure) and have Ψn(x, t) = 0 elsewhere , for n=2 , 4 , 6 etc I have got the expectation value of momentum for ⟨p⟩ and ⟨p 2⟩ for n = 2 (see figures) By direct substitution, show that the wavefunction in the figure satisfies the timedependent Schrodinger equation (provided that En takes the value derived in figure).arrow_forwardPROBLEM 2. Consider a spherical potential well of radius R and depth Uo, so that the potential is U(r) = -Uo at r R. Calculate the minimum value of Uc for which the well can trap a particle with l = 0. This means that SE at Uo > Uc has at least one bound ground state at l = 0 and E < 0. At Ug = Uc the bound state disappears.arrow_forwardSolve the following.arrow_forward
- A quantum mechanical particle is confined to a one-dimensional infinite potential well described by the function V(x) = 0 in the region 0 < x < L, V(x) = ∞ elsewhere. The normalised eigenfunctions for a particle moving in this potential are: Yn(x) = √ 2 Nπ sin -X L L where n = 1, 2, 3, .. a) Write down the expression for the corresponding probability density function. Sketch the shape of this function for a particle in the ground state (n = 1). b) Annotate your sketch to show the probability density function for a classical particle moving at constant speed in the well. Give a short justification for the shape of your sketch. c) Briefly describe, with the aid of a sketch or otherwise, the way in which the quantum and the classical probability density functions are consistent with the correspondence principle for large values of n.arrow_forwardThe wave function for the first excited state y, for the simple harmonic oscillator is y, = Axe (ax-/2), Normalize the wave function to find the value of the constant A. (Use the following as necessary: a) A%3D Determine (x), (x-), and y (x2) - (x)². (Use the following as necessary: a) (x) (x?) V (x?) - (x)? : Need Help? Read Itarrow_forwardI need the answer as soon as possiblearrow_forward
- Let's consider the two-qubit state 3 |) = 100)+101) +110). a) Find the expectation values for the values of both qubits separately. b) The product of qubit values is represented by the operator b₁b2 = (ô× 1) (I Øô) = (ô ❀ô), where bn is the observable for the value of qubit n. Find the expectation value for the product. For statistically independent quantities the expectation value of their product is the product of their expectation values. Are the values of the qubits correlated in state |V)? c) Show that the state cannot be expressed as a product state, i.e., it is an entangled state.arrow_forwardApply the boundary conditions to the finite square well potential at x = L to find the following. (a) the relationships among the coefficients B, C, and D due to boundary conditions (Use the following as necessary: a, k, L, C and D.) Y is continuous B = is continuous dx B = (b) the ratio C/D (Use the following as necessary: a, k, and L.)arrow_forwardA particle of mass m is found in a finite spherical potential well of the form S-Va V(r) = (1) F'incd the: gronnd state by solving the radial cquation for !– 0. (b) Show that there are no bound states in the case where Voa² < (Th) /8m. Hint: note that to solve the problem you obtain a transcendental equation which you must solve numerically. Use the change of variable 20 = av av2mVa/h, z = av-2mE/h.arrow_forward
- The odd parity eigenstates of the infinte square well , with potential V = 0 in the range −L/2 ≤ x ≤ L/2, are given by : (see figure) and have Ψn(x, t) = 0 elsewhere , for n=2 , 4 , 6 etc I have got the expectation value of momentum for ⟨p⟩ and ⟨p 2⟩ for n = 2 (see figures) Determine the uncertainty in momentum, ∆p, for a particle with n = 2, and use your result to put a lower bound on the uncertainty in position via Heisenberg’s uncertainty relation.arrow_forwardConsider the scattering of a particle by a regular lattice of basis a, b, c. The interaction with the lattice can be written as V = E, V(Ir – r,|). where V (r-r,|) is the potential of each atom and is spherically symmetric about the atom's lattice point. Show using the Born approximation that the condition for non-vanishing scattering is that the Bragg law be satisfied.arrow_forwardConsider a state function that is real, i.e., such that y (x) = y* (x). Show that (p) Under what conditions on p (x), would the function o (p) turn out to be real, and if so, what is (x) worth? = 0. What happens in that case with (p2) and with (x) ?;arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning