a particle is confined to move on a circle's circumference (particle on a ring) such that its position can be described by the angle ϕ in the range of 0 to 2π. This system has wavefunctions in the form Ψm(ϕ)= eimlϕ where ml is an integer. Show that the wavefunctions Ψm(ϕ) with ml= +1 and +2 are ORTHOGONAL

a particle is confined to move on a circle's circumference (particle on a ring) such that its position can be described by the angle ϕ in the range of 0 to 2π. This system has wavefunctions in the form Ψm(ϕ)= eimlϕ where ml is an integer. Show that the wavefunctions Ψm(ϕ) with ml= +1 and +2 are ORTHOGONAL

Related questions

Q: 2. The Heisenberg uncertainty principle demonstrate the symmetry between the particles position and…

Q: A particle is free to move in one dimension. At the time of t = 0, it is known that the wave…

Q: ) Simple quantum systems: potential barrier Consider a uniform potential barrier of height vp = 6 eV…

A: (1) for alpha particleEquation for transmission probability;…

Q: Use the variational principle to calculate an es rgy of the quartic oscillator. The potential of the…

A: The trial wave function is given as ϕx=e-αx22. The potential is given as V(x)=cx4. First normalize…

Q: 2) Wave function in momentum space (p) and probability density

Q: Two positive point charges are a fixed distance apart. The sum of their charges is QT Part A What…

A: The electrostatic force between two point charges separated by some distance r is given as…

Q: All parts of this problem refer to the harmonic oscillator. A) Use the expressions for the operators…

A: Given data : Harmonic oscillator xˆ and pˆ are Hermitian operators To find : A) Use the…

Q: Please, I want to solve the question correctly, clearly and concisely

A: The problem involves analyzing a thin-walled hollow quadratic (HQ) beam subjected to a vertical…

Q: What is Bloch theorem and equation. Can you describe the parameters in the bloch equation and what…

Q: Which of a, b or c is most likely to be correct? J Hint: Romombor tho roguirod rtiog of rono

A: Wavefunctions Wavefunctions are mathematical functions that encode the properties of a particle. The…

Q: Please, I want a solution to all paragraphs correctly and clearly. I sent it 3 times and did not get…

A: thank you

Q: SECTION B Answer TWO questions from Section B Question B1 Consider a finite potential step as shown…

Q: Consider a finite potential step as shown below, with V = V0 in the region x 0. Particles with…

A: The potential is given by,

Q: The wavefunction below is an eigenfunction of tje following operator. What is the corresponding…

A: Given: Operator theta and the wavefunction Psi.

Q: A particle in the ground state of the quantum harmonic oscillator, which is described by the…

Q: A thin solid barrier in the zy-plane has a 8.0-um-diameter circular hole. An electron traveling in…

A: We have a solid barrier in x-y plane with diamete hole.An electron with vx =0 passes through the…

Q: An infinite time-harmonic electric current sheet flows on the z=0 plane at the interface between two…

Q: For the following potential V(x) = --sech? x m 4o(x) = sech(x) 1) Prove that is a solution of bound…

Q: QUESTION 2 Hermite polynomials are useful for solving for the wave functions of a 3-dimensional…

A: The wave function of the three-dimensional harmonic oscillators is given in terms of the Hermite…

Q: Question A3 A wavefunction takes the form = A sin(2x) in the interval -1 < x < 1, and is zero…

A: Step 1: Step 2: Step 3: Step 4:

Q: Draw and label the potential in the table on the right. Show the Wave Function, Y, expected in each…

A: This is very simple but conceptual problem in quantum mechanics. The solution of the Schrondinger…

Question

a particle is confined to move on a circle's circumference (particle on a ring) such that its position can be described by the angle ϕ in the range of 0 to 2π. This system has wavefunctions in the form Ψ_m(ϕ)= e^imlϕ where ml is an integer. Show that the wavefunctions Ψ_m(ϕ) with ml= +1 and +2 are ORTHOGONAL

Show full and complete procedure. Do not skip any step

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1: Step 1

VIEW

Step 2: Step 2

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Just need problem 4
a particle is confined to move on a circle's circumference (particle on a ring) such that its position can be described by the angle ϕ in the range of 0 to 2π. This system has wavefunctions in the form Ψm(ϕ)= eimlϕ where ml is an integer. Show that the wavefunctions Ψm(ϕ) with ml= +1 and +2 are ORTHOGONAL Show full and complete procedure. Do not skip any step
Consider a wavefunction Ψ0 prepared at t = 0 in an infinite square well of width L, such that Ψ0 = N in the interval −L/8 < x < L/8 and is zero otherwise, as illustrated below. found in image Figure 3: A wavefunction Ψ0, prepared in an infinite square well at time t = 0. a) Derive an expression for the normalization constant N, in terms of L. b) The wavefunction of this system at time t can be written as Ψ(x,t) = Pn cnψn(x)e−iEnt/~, where {cn} are a set of constants and {ψn(x)} are the set of energy eigenstates of the well. Use this equation to derive an expression for the cn in terms of Ψ0 and ψn(x). c) The energy eigenstates in the infinite square well are given by found in image Use these equations to derive expressions for the first five of the cn defined in part b) (i.e. derive expressions for c1, c2, c3, c4 and c5). d) Calculate new expressions for the cn if the constant initial wavefunction Ψ0 were changed so that it was restricted to have non-zero values…
a particle is confined to move on a circle's circumference (particle on a ring) such that its position can be described by the angle ϕ in the range of 0 to 2π. This system has wavefunctions in the form Ψm(ϕ)= eimlϕ where ml is an integer. Show that the wavefunctions Ψm(ϕ) with ml= +1 and +2 are ORTHOGONAL Show full and complete procedure. Do not skip any step
Use your generic solution to the 2D box wavefunctions to demonstrate the following prop- erties of wavefunctions. 1. Show that if you independently normalize (x) and (y) that the product of (x) and (y) is also normalized. 2. Show that the wavefunctions for one dimension are orthogonal. Orthogonality means that f₁ Vndr = Smn, where the Kroenecker delta function means that the function is one for men and zero for m‡n. m 3. How many quantum numbers are needed to describe the energy of your system? 4. Show that the two dimensional wavefunctions are orthogonal by performing this test on the wavefunction for n = 1, ny = 2 and the wavefunction for nr = 2 and ny = 1. CLx Ly Mathematically the operations looks like f¹* f¹¹ V₁,2 (x, y) V2,1 (x, y) dxdy.
what are the possible results that may be obtained upon measuring the property lz on a particle in a particular state, if its wavefunction is known to be Ψ, which is an eigenfunction of l2 such that l2Ψ=12ℏΨ? SHOW FULL AND COMPLETE PROCEDURE IN A CLEAR AND ORDERED WAY