Exercise 4Problem 4.15 A hydrogen atom starts out in the following linear combination ofthe stationary states n = 2, 1 = 1, m 1 and n 2, 1 1, m = -1:1V(r. 0) =(211+ V21-1).(a) Construct (r, t). Simplify it as much as you can.(b) Find the expectation value of the potential energy, (V). (Does it depend onr?) Give both the formula and the actual number, in electron volts.

Part (a) Given: The linear combination of first state is n=2,l=1,m=1. The linear combination of…

Problem 4.15 A hydrogen atom starts out in the following linear combination of the stationary states n = 2, 1 = 1, m 1 and n 2, 1 1, m = -1: V(r. 0) = 1 (W211+V21-1). (a) Construct V(r, t). Simplify it as much as you can. (b) Find the expectation value of the potential energy, (V). (Does it depend on t?) Give both the formula and the actual number, in electron volts.

Problem 4.15 A hydrogen atom starts out in the following linear combination of the stationary states n = 2, 1 = 1, m 1 and n 2, 1 1, m = -1: V(r. 0) = 1 (W211+V21-1). (a) Construct V(r, t). Simplify it as much as you can. (b) Find the expectation value of the potential energy, (V). (Does it depend on t?) Give both the formula and the actual number, in electron volts.

Related questions

Q: A particle moves in a one-dimensional box with a small potential dip E(0) ²² 2m/2 Quortion 4 V= ∞o…

Q: PROBLEM 1. Calculate the normalized wave function and the energy level of the ground state (l = 0)…

A: Given: The radius of the infinite spherical potential is R. The value of Ur=0 r<RUr=∞…

Q: Consider a particle of mass u, whose Hamiltonian is: p2 1 Ho = 27+R² Но (an isotropic…

A: Required to find the energy levels of the quantum system

Q: Problem 1.17 A particle is represented (at time=0) by the wave function A(a²-x²). if-a ≤x≤+a. 0,…

Q: Find the norm of each of the following functions on the given interval and state the normalized…

A: we need to evaluate the integral of the square of the function over the interval, and then take the…

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: REQUIRED Consider the one dimensional harmonic oscillator. (a) Prove that (b) Prove that (c) Prove…

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

Q: Consider a cubic 3D infinite well. part a: How many different wave functions have the same energy as…

A: Therefore, the entirety of the observed degeneracy in this system can be attributed to…

Q: Exercise 5.10 Consider the operator Â = ½ (ĴxĴy + ĴyĴx). (a) Calculate the expectation value of Â…

Q: Consider a particle in a one-dimensional rigid box of length a. Recall that a rigid box has U (x) =…

Q: Use a trial function of the form e(-ax^2)/2 to calculate the ground state energy of a quartic…

Q: please provide detailed solution for a to c, thank you

A: thank you

Q: 6. In lecture we considered the infinite square well located from 0 1/1/201 a) Determine the…

Q: #1: Find the time depended wave functions V(x, t) = ?

Q: 2. Determine the transmission coefficient for a rectangular barrier (same as [Grf] Equation 2.148,…

Q: 7. 1. Calculate the energy of a particle subject to the potential V(x) Vo + câ/2 if the particle is…

Q: ηπχ sin (1x). If L = 10.0, what is the L The eigenstates of the particle-in-a-box are written, n =…

Q: Problem 4. Consider the rigid rotor of problem 3 above. A measurement of Le is made which leaves the…

Q: Question 2 2.1 Consider an infinite well for which the bottom is not flat, as sketched here. If the…

Q: *Problem 1.3 Consider the gaussian distribution p(x) = Ae¯ e-^(x-a}² where A, a, and A are positive…

Q: A particle is confined betweek = 7). Evaluate the probability to find the particle in an interval of…

A: Given: The length of the rigid wall is L=0.189 nm. The state of the particle is n=7. The…

Q: Problem 2.13 A particle in the harmonic oscillator potential starts out in the state Y (x. 0) =…

A: (a) Normalization condition to determine the A value,…

Question

Exercise 4
Problem 4.15 A hydrogen atom starts out in the following linear combination of
the stationary states n = 2, 1 = 1, m 1 and n 2, 1 1, m = -1:
1
V(r. 0) =
(211+ V21-1).
(a) Construct (r, t). Simplify it as much as you can.
(b) Find the expectation value of the potential energy, (V). (Does it depend on
r?) Give both the formula and the actual number, in electron volts.

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

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

Why don't you include the time dependent part of the wave equation when finding the expectation value of the potential? I don't see how the modulus of the wave function gets rid of the time dependent part. Can you please explain?

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

There is an electron, in a 1-d, infinitely deep square potential well with a width of d. If it is in ground state, 1. Draw the electron's wavefunction. Show the position of the walls of the potential well. 2. Explain how the probability distribution for detecting the electron at a given position differs from the wavefunction.
By employing the prescribed definitions of the raising and lowering operators pertaining to the one-dimensional harmonic oscillator: x = ħ 2mω -(â+ + â_) hmw ê = i Compute the expectation values of the following quantities for the nth stationary staten. Keep in mind that the stationary states form an orthogonal set. 2 · (â+ − â_) [ pm 4ndx YmVndx = 8mn a. The position of particle (x) b. The momentum of the particle (p). c. (x²) d. (p²) e. Confirm that the uncertainty principle is satisfied for all values of n
2. A simple harmonic oscillator is in the state 4 = N(Yo + λ 4₁) where λ is a real parameter, and to and ₁ are the first two orthonormal stationary states. (a) Determine the normalization constant N in terms of λ. (b) Using raising and lowering operators (see Griffiths 2.69), calculate the uncertainty Ax in terms of .
11. Evaluate (r), the expectation value of r for Y,s (assume that the operator f is defined as "multiply by coordinate r).Why does (r) not equal 0.529 for Y,,? In this problem,use 4ardr = dt.
The Hamiltonian for the one dimensional quantum oscillator is 1 p² 1 Ĥ = 1² + ½ k²² = 12 + √ mw² à² 2m 2m 2 where k = mw². 1) Define the operators ₁₁ and ₁₁ such that Ĥ = ½ħw (p² + ²). Define Ĥ2 as a function of 1 and p₁ such that Ĥ = hwĤ₂. - 2) Let us define the new operators â (1 + i₁) and â† = ½(î₁ — ip₁). Express ₁ and p₁ as a function of â and â³. Knowing that [^^1,î₁] = i and [1, 1] = -i, calculate âât and â†â. Express Ĥ2 as a function of a and at. 3) Let us define Ñ such that Ĥ₂ = Ñ + ½. Knowing that Ĥ, Ĥ₂ and Ñ have the same eigenstates, what are their corresponding eigenvalues?
For the Osaillator problem, mwx2 har monit (부) (2M) y e Y, LX) = Mw 1. Use the lowering operator to find Yo(X). 2. Is your wave function normalized ? Check.
Exercise 6.4 Consider an anisotropic three-dimensional harmonic oscillator potential acy = { m (w² x ² + w} y² + w? 2²). V (x, y, z) = = m(o² x² + @z. (a) Evaluate the energy levels in terms of wx, @y, and (b) Calculate [Ĥ, Î₂]. Do you expect the wave functions to be eigenfunctions of 1²? (c) Find the three lowest levels for the case @x = @y= = 2002/3, and determine the degener- of each level.
2. Consider the potential shown: -kx, x 0 2 where k is a positive constant. Call the ground state energy eigenfunction of this well ₁(x), with energy E₁. The fourth excited state would be called 45(x), with energy E5. In your answers to the questions below, please indicate in words interesting features, e.g. sign of concavity, where zeros are, where there is decay or oscillation, forbidden regions, etc. (a) Sketch the ground state, 4₁(x), (b) Sketch the excited state, 45(x) V(x) I I V(x) I x=0 E5 E₁
Consider the half oscillator" in which a particle of mass m is restricted to the region x > 0 by the potential energy U(x) = 00 for a O where k is the spring constant. What are the energies of the ground state and fırst excited state? Explain your reasoning. Give the energies in terms of the oscillator frequency wo = Vk/m. Formulas.pdf (Click here-->)
O Consider the kinetic energy matrix elements between Hydrogen states (n' = 4, l', m'| |P|²| m -|n = 3, l, m), = for all the allowed l', m', l, m values. What kind of operator is the the kinetic energy (scalar or vector)? Use this to determine the following. For what choices of the four quantum numbers (l', m', l, m) can the matrix elements be nonzero (e.g. (l', m', l, m) (0, 0, 0, 0),...)? Which of these nonzero values can be related to each other (i.e. if you knew one of them, you could predict the other)? In this sense, how many independent nonzero matrix elements are there? (Note: there is no need to calculate any of these matrix elements.)
I need the answer as soon as possible
d² Let Â = Consider the orthonormal basis: dx² |1) = ₁(x) = [2) = ₂(x) = √sin(x) L 2π sin and (a) Find Â1) and Â12). The operator Â can be expressed in a matrix form as follows: Â = a₁1)(1| + a₁21)(2 + a21 2)(1| + a2212X<21. (b) Use part (a) to compute: amn= (m|Â\n); m, n = 1,2.