You are given a free particle (no potential) Hamiltonian ÎI -dependent wave-functions=₁(x, t)V₂(x, t)=-it 2h²m=ħ² d²2m dx2sin(27x)e-it2 sin(x)eit + sin(2x)e¯hn 2• Are V₂(x, 0) eigenfunctions of Ĥ ? (give explanation for each case)and two time--it 2hr 2m(1)(2)

Answered: Image /qna-images/answer/a62752be-3980-4a5d-8d8b-5bd0ad079c6f.jpg

You are given a free particle (no potential) Hamiltonian Ĥ dependent wave-functions ₁(x, t) V₂(x, t) = - = ħ² d² 2m dx2 sin(27x)e-it 2² m In ² 2 sin(x)e-it! 2m + sin(27x)e¯ ● Are V₁(x,0) eigenfunctions of Ĥ ? (give explanation for each case) and two time- -it 2h 2 m (1) (2)

You are given a free particle (no potential) Hamiltonian Ĥ dependent wave-functions ₁(x, t) V₂(x, t) = - = ħ² d² 2m dx2 sin(27x)e-it 2² m In ² 2 sin(x)e-it! 2m + sin(27x)e¯ ● Are V₁(x,0) eigenfunctions of Ĥ ? (give explanation for each case) and two time- -it 2h 2 m (1) (2)

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

See similar textbooks

Related questions

Q: -E7D.5(b) Calculate the probability that a particle will be found between 0.65L and 0.67L in a box…

A: In the given question we have to calculate the probability of finding a particle between 0.65L and…

Q: Find the eigenvalue of operating on the function f(x) = Asin(nx) + Bcos(mx) with the following…

Q: Calculate the expectation values of px and px2 for a particle in the state with n = 2 in a…

A: Where, H is the Planck’s constant The wave function for n = 2 in a square well potential is given by…

Q: Assume that the states of the π electrons of a conjugated molecule can be approximated by the…

A: SOLUTION: Step 1: For a particle in one dimensional Box, the normalized Wave function is

Q: %3D 2n do 4. Determine whether the following orbitals are eigenfunctions of l. (1, = -i- If yes,…

Q: 2. (a) Determine the normalization.constant for the particie in a box atypical wave function th…

A: A normalized wave function has Total probability over a integral with in limit is equal to one. A…

Q: The wave function for the ground state of the harmonic oscillator is %0 (2) = Ce-mw/(2A)|z² where C…

A: In the given question the ground state of the hormonic oscillator is given in unnormalised form,…

Q: 8C.4 (a) the moment of inertia of a CH4 molecule is 5.27 x 10^-47 kg m^2. What is the minimum energy…

A: The answer for first question is given below. Kindly repost the other question as separate one

Q: Determine the value of the orbital, L, spin, S, total angular momentum J and g, for the ions Pr³+…

A: The given ions are Pr^3+ and Yb^3+.Here L is orbital angular momentum..S is Spin angular momentum.J…

Q: For the system described in Exercise E7B.1(a) (A possible wavefunction for an electron in a region…

Q: The normalized wave function for a particle in a one- dimensional box in which the potential energy…

Q: Ch

Q: Consider the wave function V222(x, ỹ, z) for a particle in a cubic box. Figure 4.45a shows a contour…

A: (a)

Q: You are given a free particle (no potential) Hamiltonian Ĥ = dependent wave-functions V₁(x, t)…

Q: Please answer both questions!! Please make sure it's handwritten and legible!!!

A: Approach to solving the question: Detailed explanation: Examples: Key references: read macquirre…

Q: The wavefunction of one of the d orbitals is proportional to sin2θ sin 2ϕ. At what angles does it…

Q: What is the eigenvalue for the eigenfunction e^(3√3ix) ?

A: This problem is based on quantum chemistry. The solution is given below.

Q: P7E.5 In infrared spectroscopy it is common to observe a transition from the v = 0 to v = 1…

A: Hi. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If you…

Q: Determine whether or not the state 211 is an eigenfunction of the operator V2, and if so, give the…

A: The objective of the question is to determine if the state 211 is an eigenfunction of the operator…

Q: Evaluate Δx = (⟨x2⟩ − ⟨x⟩2)1/2 and Δpx = (⟨px2⟩ − ⟨px⟩2)1/2 for the ground state of (a) a particle…

Q: calculate the energy needed excite a CH4 molecule from a state with l=1 to a state with l=2

Q: Consider a particle in the following 1D box. The potential in this box has the form: 1 2. V = kx² 2…

Q: Consider a particle trapped in a 1D box with zero potential energy with walls at x = 0 and x = L.…

A: Potential energy (V) is the energy possessed by the electron or any object due to its position which…

Q: The wave functions p. and d are linear combinations of the spherical harmonic functions, which are…

A: The angular portion of the wave functions for the px and dxz orbitals of the hydrogen atom are…

Q: E7B.3(b) Which of the following functions can be normalized (in all cases the range for x is from x…

A: The answer for this problem is provided below in great details within the attached figures.

Q: Calculate the expectation value of the radius (r) at which you would find the electron if the H atom…

Q: 4. Given these operators A=d/dx and B=x², can you measure the expectation values of the…

A: We have to use the concept of commutator over here. If the given observable commute with each other,…

Q: 8. Do the linear momentum operator px and angular momentum operator Lx commute. Can the velocity in…

Concept explainers

Quantum Chemistry

Quantum chemistry deals with the properties of chemical systems and their reactions. The branch of chemistry which is more concerned with quantum chemistry is physical chemistry. It is a more sophisticated field of theoretical physics which is concerned towards the application of physical concepts towards various chemical aspects such as, formation of atoms, chemical structure descriptions, chemical bond strength, hybridization, conjugation etc. Quantum chemistry mainly studies the various states i.e., ground state, excited state, transition states of the individual atoms or molecules taking place during any chemical reaction. The laws of motion explained by various scientists, which are termed as “classical mechanics” were not acceptable in terms of electrons, protons, atoms, light etc. Thus, a new theory named “quantum mechanics” emerged to understand the basic framework of various atomic and subatomic particles.

Question

You are given a free particle (no potential) Hamiltonian ÎI -
dependent wave-functions
=
₁(x, t)
V₂(x, t)
=
-it 2h²
m
=
ħ² d²
2m dx2
sin(27x)e-it
2 sin(x)eit + sin(2x)e¯
hn 2
• Are V₂(x, 0) eigenfunctions of Ĥ ? (give explanation for each case)
and two time-
-it 2hr 2
m
(1)
(2)

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: Concept used

VIEW

Step 2: solving equation a

VIEW

Step 3: For second equation

VIEW

Solution

VIEW

Step by step

Solved in 4 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Introduction and Principles of Quantum Theory

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.

Similar questions

None
J J 8a. What is the expectation value of the linear momentum for the 1-D wavefunction: -ax² (x)= Ne where 0
(a) For a particle in the stationary state n of a one dimensional box of length a, find the probability that the particle is in the region 0xa/4.(b) Calculate this probability for n=1,2, and 3.
3) Consider an arbitrary operator A. A operates on any function to its right. Here are the results of this operator on three different functions: Af(x, y, z) = hf(x, y, z) AY(0) = 04(0) ÂY(x) = Y(x) Which of the functions are eigenfunctions of Â?
5. (McQuarrie 9-25) Show that the atomic determinantal wave function, 1 1sa (1) 1sẞ(1) V(r1, r2)= √2 1sa (2) 1sẞ(2) is normalized when the 1s orbitals are normalized. Hint: Don't freak out about this problem-it's easier than it looks! Expand the Slater determinant to get the wavefunction in a more usable form, then set up the normalization integral for . Multiply everything out, and you should have complicated-looking integrals such as this: (1sa (1) 1sẞ(2) | 1sa(1) 1sẞ(2)) While such integrals might look scary, they're actually straightforward. An integral like the one above has four pieces: integration over (a) the spatial coordinates of electron 1, (b) the spatial coordinates of electron 2, (c) the spin coordinates of electron 1, and (d) the spin coordinates of electron 2. You can break up these multi-dimensional integrals into separate integrals for each piece. For example: (1sa (1) 1sẞ(2) | 1sa(1) 1sẞ(2) ) = (1s(1)|1s(1)) · (a(1)|a(1)) · (1s(2)|1s(2)) · (6(2)|ß(2)) Then you can…
What is the answer
What is the eigenvalue for the eigenfunction e^(-2√3) ?
The wavefunction for the 2s orbital of a hydrogen atom is N((2-r)/a0)e-r/2a0. Evaluate the normalization constant N.
Consider again the system in quizzes 1 and 2, namely a particle moving in one dimension described by the normalized wavefunction (x) = 30 1 (а — х) for 0 a . а Determine the expectation value () for the particle.
1 Find the eigenvalues and eigenstates of the spin operator S; of an electron in the direction of a unit vector n; assume that n; lies in the yz plane. Find the probability of measuring S, = -
please answer part c in details
Identify the normalized wavefunction for a particle rotating about the surface of a sphere with a fixed radius with I= 1 and mj = ±1. 1 3 e tiø Psine 2 V 2 1 y =, 土ゆ 2 T 3 sine e tip 2