Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 2.2, Problem 2.4P
To determine
The
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
This is a problem in the field of quantum mechanics.
Find the normalization constant A [in Equation Ψ(x, y, z) = A sin(k1x)sin(k2y)sin(k3z) ] for the first excited state of a particle trapped in a cubical potential well with sides L. Does it matter which of the three degenerate excited states you consider?
Assume that you have a quantum mechanical observable N with eigenvalues
Wi and corresponding eigenvectors |w;). Show that
(n?) – (N)²
where P(w;) is the probability of measuring the eigenvalue w; for some quantum state.
Chapter 2 Solutions
Introduction To Quantum Mechanics
Ch. 2.1 - Prob. 2.1PCh. 2.1 - Prob. 2.2PCh. 2.2 - Prob. 2.3PCh. 2.2 - Prob. 2.4PCh. 2.2 - Prob. 2.5PCh. 2.2 - Prob. 2.6PCh. 2.2 - Prob. 2.7PCh. 2.2 - Prob. 2.8PCh. 2.2 - Prob. 2.9PCh. 2.3 - Prob. 2.10P
Ch. 2.3 - Prob. 2.11PCh. 2.3 - Prob. 2.12PCh. 2.3 - Prob. 2.13PCh. 2.3 - Prob. 2.14PCh. 2.3 - Prob. 2.15PCh. 2.3 - Prob. 2.16PCh. 2.4 - Prob. 2.17PCh. 2.4 - Prob. 2.18PCh. 2.4 - Prob. 2.19PCh. 2.4 - Prob. 2.20PCh. 2.4 - Prob. 2.21PCh. 2.5 - Prob. 2.22PCh. 2.5 - Prob. 2.23PCh. 2.5 - Prob. 2.24PCh. 2.5 - Prob. 2.25PCh. 2.5 - Prob. 2.26PCh. 2.5 - Prob. 2.27PCh. 2.5 - Prob. 2.28PCh. 2.6 - Prob. 2.29PCh. 2.6 - Prob. 2.30PCh. 2.6 - Prob. 2.31PCh. 2.6 - Prob. 2.32PCh. 2.6 - Prob. 2.34PCh. 2.6 - Prob. 2.35PCh. 2 - Prob. 2.36PCh. 2 - Prob. 2.37PCh. 2 - Prob. 2.38PCh. 2 - Prob. 2.39PCh. 2 - Prob. 2.40PCh. 2 - Prob. 2.41PCh. 2 - Prob. 2.42PCh. 2 - Prob. 2.44PCh. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - Prob. 2.47PCh. 2 - Prob. 2.49PCh. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 2 - Prob. 2.52PCh. 2 - Prob. 2.53PCh. 2 - Prob. 2.54PCh. 2 - Prob. 2.58PCh. 2 - Prob. 2.63PCh. 2 - Prob. 2.64P
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
- A qubit is initially in state [0). Its state is then transformed by the unitary operation represented by the matrix U ¹ = ¹2 ( √3³ √ ) = √³ (10) (0) + (1¹) (11) + ½ (10) (1| + (1) (01) . a) What is the probability of the qubit to have the value 0 when measured before the transforma- tion? How about the value 1? b) What is the probability of the qubit to have the value 0 when measured after the transforma- tion? How about the value 1? c) Let's say that the qubit is measured after the transformation, and its value is found to be 1. What is the probability of the qubit to have the value 0 immediately after the measurement?arrow_forwardA system is in an eigenstate |m, l) of the angular momentum operators L2 and L2. Calculate the expectation values of (L) and (L²), and (Ly) and (L3).arrow_forwardwhere 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=0₁arrow_forward
- (c) Consider a system of two qubits with canonical basis states {|0) , |1)}. Write down an example for a two- qubit density matrix corresponding to a separable pure state and an example for a two-qubit density matrix corresponding to an entangled pure state.arrow_forwardA quantum gate U performs the following mapping on the Z-basis (standard/computational basis) states: (a) (b) BE 2√3 Joy 2√3 1). 2√3 2√3 Find the matrix representation of U in Z-basis and show that U is a valid quantum gate. Evaluate HUH|0).arrow_forwardLet'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_forward
- Consider a particle of mass m in a one-dimensional infinite square well with V(x) = 0 for 0 ≤ x ≤ a and V(x) = elsewhere. A time-dependent perturbation is added of the form 2x V₁(x,t) = = ε - 1 sin(wt) for 0 ≤ x ≤ a a = ∞ If initially the particle is in the ground state, calculate the probability that it will make a transition to the first excited state.arrow_forwardH. Mc | 4 — 14₁7 — 19₂ > > 1917 of orthonormal eigen state Q Consider astate >= which as given interm 3 14 > 10 > 1437 of an operator B such that 19 B² | o₂ >= n² | On> find the expectation value of B² bearrow_forwardThe harmonic oscillator eigenfunction ₁(x) = = 4a³\1/4 e-ax²/2, where a = μω ħ (a) Find (x²) for an oscillator in this state, and express your result in terms of u, w, and ħ. 1 (b) In an eigenstate it is always true that (T) = (V) for a harmonic oscillator. If ↑ =-=-=-=A² 2μ 1 and ✩ = µw²x², find (p²) when the system is in the state 1₁ (x). (Note: You can use the result found in part (a), or compute it directly from the form of the operator p.) 2arrow_forward
- Consider the function v(1,2) =( [1s(1) 3s(2) + 3s(1) 1s(2)] [x(1) B(2) + B(1) a(2)] Which of the following statements is incorrect concerning p(1,2) ? a. W(1,2) is normalized. Ob. The function W(1,2) is symmetric with respect to the exchange of the space and the spin coordinates of the two electrons. OC. y(1,2) is an eigenfunction of the reference (or zero-order) Hamiltonian (in which the electron-electron repulsion term is ignored) of Li with eigenvalue = -5 hartree. d. The function y(1,2) is an acceptable wave function to describe the properties of one of the excited states of Lit. Oe. The function 4(1,2) is an eigenfunction of the operator S,(1,2) = S;(1) + S,(2) with eigenvalue zero.arrow_forwardThe coherent states for the one-dimensional harmonic oscillator are defined as eigenstates of the operatorof annihilation a (which is non-Hermitian):a |λ⟩ = λ |λ⟩ (1)where λ is a complex number in general. a)prove that is a normalized consistent state. b)Show that the above state satisfies the minimum uncertainty relation, i.e., show thatarrow_forwardStarting with the equation of motion of a three-dimensional isotropic harmonic ocillator dp. = -kr, dt (i = 1,2,3), deduce the conservation equation dA = 0, dt where 1 P.P, +kr,r,. 2m (Note that we will use the notations r,, r2, r, and a, y, z interchangeably, and similarly for the components of p.)arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON