show hamiltonian operator for the plane waves (exponential, imaginary) Prove that this operator does not change this function. Prove that this operator does generate energy of a particle in free space.

show hamiltonian operator for the plane waves (exponential, imaginary) Prove that this operator does not change this function. Prove that this operator does generate energy of a particle in free space.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.23P

See similar textbooks

Related questions

Q: What is the Hamiltonian of a system? Show that the kinetic energy operator commutes with the linear…

A: The momentum operator in 1D is defined as px=-ihδδx the Kinetic energy operator is Tx=-h22mδ2δx2…

Q: In class, we developed the one-dimensional particle-in-a-box model and showed that the wavefunction…

Q: Given that A is Hermitian operator P'rove hat (a) The cigenvalues of operator A are real (b) The…

A: Given A is Hermitian operator.

Q: Asynchronous Activity Consider a particle of mass m moving freely in a conservative freely in a…

Q: Shortest Line in 3D Prove that the shortest path between two points in 5. three dimensions is a…

A: The distance between the two points in the three dimensions can be given as follow:

Q: Demonstrate that in an electromagnetic field, the gauge transformation transfers the L to an…

A: I wrote an answer in a Page:

Q: a- Construct the 2-dimensional matrix A that representing the effect of operator Â on the…

Q: A ball of mass m, slides over a ếy sliding inclined plane of mass M and angle a. Denote by X, the…

A: The expression for the degree of freedom is given as, F=3N-K Here, N is the number of particles,…

Q: nian is given by H = p2/2m + m[omega]2x2/2. a) Determine the Ehrenfest equations of motion for and…

Q: 2. The wavefunctions for the particle in a 1-D box are given as Pn (X) = , nTX sin (a) Show that…

Q: Using the del operator in tesian coordinates to derive the operator in the cylindrical

Q: Show that if the Hamiltonian and a quantity F are constants of motion, then af/at is also a…

Q: Show that the momentum Operator is a Operator, or (W/P/V); is real number. is Hermition

A: We know that momentum operator is given by P^=-ihddr where r is the position coordinate and h is the…

Q: The energy of the Hamiltonian operator defined below for the one-dimensional anharmonic oscillator…

A: The first-order energy correction using Perturbation theory for some nth level is given as: The…

Q: Show that the function ψ = 8e5x is an eigenfunction of the operator d/dx. What is the eigenvalue?…

Q: 1. Find the Matrix that represents the operator of the second derivative with respect to position.…

Q: Q1: (1 0 0 The Hamiltonian is represented by the matrix H = 0 0 2 0 0 0 2 Where o is positive real…

Q: For the motion of a projectile write the Lagrangian and the Hamiltonian functions in polar…

A: The Lagrangian of a system is defined as:L=T-V………(1)where,T is the Kinetic energy.V is the Potential…

Q: a- Construct the 2-dimensional matrix A that representing the effect of operator Â on the…

Q: Find the equations of motion for the Lagrangian L = eγt(mq˙2/2 − kq2/2) How would you describe the…

Q: Define ond nlustrate general collis fons of two objects two- dimensional space. Please define the…

A: According to momentum conservation: Particles momentum before collision must be same as particle's…

Q: 3. In each case, show that f (x) is an eigenfunction of the operator given. Find the eigenvalue.…

Q: Q.6) Read the quest ions carefully and choose the correct option: (i) The Hamiltonian funct ion in…

A: In the given question, We have to discuss about Hamiltonian function.

Q: Using the condition (3.027) of Lect. 16, prove that the mo- mentum operator p is Hermitian. HINT:…

A: Condition for the operator to be Hermitian, Using the periodic boundary conditions for the functions…

Q: (a) Construct 3-dimensional matrix G that representing the action of the operator H. (b) If the…

Q: Consider the motion of a particle of mass say m. Using Cartesian coordinates as generalized…

A: This is a classical mechanics problem. Here we deduce the Lagrange's equation of motion from the…

Q: Consider the Lennard-Jones potential between atoms in a solid material. Find the dependence of the…

A: The Lennard-Jones potential is given by, V=4Eσx12-σx6 where E is the depth of the potential well or…

Q: Two mass points of mass m1 and m2 are connected by a string passing through a hole in a smooth table…

Q: Find the equations of motion for the Lagrangian L = eγt(mq˙2/2 − kq2/2) How would you describe the…

Q: A point particle moves in space under the influence of a force derivable from a generalized…

A: Classical Mechanics

Q: If a particle of mass m is in a potential that is only a function of coordinates, calculate the…

Q: Q2: 0 0 The Hamiltonian is represented by the matrix H = u 0 0 1 Where u is positive real number. 1…

Q: An anharmonic oscillator has the potential function V = 1/2.(k.x^2) + c.x^4 where c can be…

A: The additional terms cx4 is the perturbation to the idea, harmonic oscillator. Energy correction to…

Q: Use the Euler's Lagrange equationto prove clearly that the shortest distance between two points in…

Q: Find the modified wavenumber for the operator derived. Plot the real and imaginary parts of K*A vs.…

Q: If we have two operators A and B possess the same common Eigen function, then prove that the two…

Q: The only possible outcome to measure the observable is one of the eigenvalues of any operator À…

A: Yes, it is true. Eigen values of the operators are the measures to the observable.

Q: 1. Consider the matrix operator A = 2. 1. 4 2. a. Show that 3 is one of its eigenvalues, b. Find the…

A: Given: A=-2-42-212425

Q: Show that the position operator (Ê = x) and the hamiltonian operator (Ĥ : -(n2/2m)d²/dx² + V (x))…

A: Proof for Position operator being hermitian x^ψψ=∫-∞∞xψ*ψdx=∫-∞∞xψ*ψdx=∫-∞∞ψ*xψdx=ψx^ψ

Q: 1) Give the Lagrange function and the Lagrangian equation(s) of motion of the second kind for the…

Q: a- Construct the 2-dimensional matrix A that representing the effect of operator Â on the…

Q: Calculate the hermitian conjugate (adjoins) for operator d/dx

Q: Show that the following operators are Hermitian, a) Momentum operator b) Hamiltonian operator c) i…

Q: Consider a particle of mass m acted upon by a central potential (r is distance and a>0 is a…

Q: Yoyo The figure below shows a crude model of a yoyo. A massless string 4. suspended vertically from…

A: The total kinetic energy of the body is

Q: Show that the operator H = -1/2(d^2/dx^2) is hermitian, assuming that it operates on a Hilbert…

Question

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

PROBLEM 2. Find the eigenvalues of a Hermitian operator represented by the following matrix: 1 i -i 1
Problem 9. For a system described by the Hamiltonian H = p°/2m + V(x), obtain an expression for d (p/2m)Idt. Discuss the relation of your result to the classical work-energy theorem.
Show that the eigen functions of the Hamiltonian operator are orthogonal and its eigen values are real.
Q#10. (a) Show that any component of the momentum operator of a particle is compatible with its kinetic energy operator. (b) Show that the momentum operator is compatible with the Hamiltonian operator only if the potential operator is constant in space coordinates.
Prove the following: if the Hamiltonian is independent of time, then ∆E doesn't change in time. Show work and be explicit to prove the statement.
A particle of mass m moves in the one-dimensional potential x2 -x/a U(x) = U, Sketch U (x). Identify the location(s) of any local minima and/or maxima, and be sure that your sketch shows the proper behaviour as x → t00. Here a is a constant.
The dynamics of a particle moving one-dimensionally in a potential V (x) is governed by the Hamiltonian Ho = p²/2m + V (x), where p = is the momentuin operator. Let E, n = of Ho. Now consider a new Hamiltonian H given parameter. Given A, m and E, find the eigenvalues of H. -ih d/dx 1, 2, 3, ... , be the eigenvalues Ho + Ap/m, where A is a %3|
Show that the operators for the x coordinate and for the kinetic energy in the x-direction TX do not commute. Calculate the operator representing the commutator.
Particle of mass m slides without friction on a wedge of angle alpha and mass M that can move without friction on a smooth horizontal surface,as shown in the figure.Treating the constraint of the particle on the wedge by the method of Lagrange multipliers,find the equation of motion for the particle and wedge.Also obtain an expression for the forces of constraint.Calculate the work done in time t by the forces of constraint acting on the particle and on the wedge.what are the constants of motion for the
Consider the following operators on a Hilbert space V³ (C): 0-i 0 ABAR-G , Ly i 0-i , Liz 00 √2 0 i 0 LE √2 010 101 010 What are the corresponding eigenstates of L₂? 10 00 0 0 -1 What are the normalized eigenstates and eigenvalues of L₂ in the L₂ basis?
The Hamiltonian of a certain system is given by 0 0 H = ħw|0 _0 0 0 1 1 Two other observables A and B are represented by A = a|-i 0 0 0 0 1 [1 0 0 B = b|0 _2 0 Lo o 2 w, a, b are positive constant. a. Find the eigenvalues and normalized eigenvectors of H b. Suppose the system is initially in the state 2c ly(0) >= 2c where c is a real constant. Determine the normalized state |4(t) >. c. What are the eigenvectors of B? d. Find the expectation values of A and B in the state [Þ(t) >, and hence determine if A and B are conservative observables
Q. 7: Prove that if the vector is the gradient of a scaler function then its integral round a closed curve is zero.