for the particle in the box, consider a state which is a linear combination of the...
for the particle in the box, consider a state which is a linear combination of the ground and the first excited states, c1(x), + c2(x). what conditions should be applied to the values of c1 and c2? what is the expected value of the energy operator (Hamiltonian) at this state?
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for the particle in the box, consider a state which is a linear
combination of the...
The eigenfunctions for a particle in a one-dimensional box of length L, and the corresponding energy...
The eigenfunctions for a particle in a one-dimensional box of length L, and the corresponding energy eigenvalues are given below. What is the variance of measurements for the linear momentum, i.e., Op = v<p? > - <p>2? Øn (x) = ( )" sin nga, n= 1, 2,.. En = n2h2 8m12 Note the Hamiltonian operator to give the energy is H = = - 42 8n72 dx2 nh 2L oo O nềh2 412 Uncertain since x is known. Following Question...
Particle with a speed bump Consider our old friend the 1D particle in the box, except...
Particle with a speed bump Consider our old friend the 1D particle in the box, except now with a speed bump in the box so the potential now is given by L and L < x < L 0, Vo 0 x V (x) otherwise (a) Calculate the first order correction to the ground state (n = 1) and first excited state (n = 2) energies (b) Calculate the first order correction to the ground state wave function in terms...
Answer all questions please 5. Consider a particle in the first excited state ofa rigid box...
Answer all questions please
5. Consider a particle in the first excited state ofa rigid box of length a. (a) Find the probability density (b) where is the particle most likely to be found? 6. Determine the wavelength of the photon emitted when an electron in a hydrogen atom makes transition from the 5 excited state to the following states (a) ground state (b) 1 excited states (c) 2 excited state Determine whether the emission is visible, uv or infrared...
64 Consider a particle in a one-dimensional box in the ground state v, and the first...
64 Consider a particle in a one-dimensional box in the ground state v, and the first excited state , described by the wave functions listed below. For each wave function, calculate the expec- tation value of the position (x), the expectation value of the position squared (), the expecta- tion value of the momentum (p), and the expectation value of the momentum squared (p2). 2 . 2x Ossa 0sxSa (b) Y2(x) = Vasin-
1. (50 points) Consider the particle in a one-dimensional box (0 s x S L). Assume a term is added to the Hamiltonian of the form: πχ V(x)g sin Sketch the potential and the expected eigenfunction (...
1. (50 points) Consider the particle in a one-dimensional box (0 s x S L). Assume a term is added to the Hamiltonian of the form: πχ V(x)g sin Sketch the potential and the expected eigenfunction (small g). In the limit of small g, find the second order correction to the ground state energy 2. (50 points) For a diatomic molecule rotating in free space, the Hamiltonian may be written: 12 21 Where L is the total angular momentum operator,...
8. Consider one electron in a 1D box of side L. Its wavefunction is given by...
8. Consider one electron in a 1D box of side L. Its wavefunction is given by из where ф1(x), фг(x), and фз(x) are the first 3 eigenfunctions of the Hamiltonian, H, of a particle in a 1D box, 2m dx2 a) Is Ψ(x) normalized? If it is not normalized it, normalize it! b) Is Ψ(x) an eigenfunction of A? If it is an eigenfunction, what is the 9. A linear polyene contains 8 -electrons, and absorbs light with412 nm. b)...
Consider an electron in a cubic box that measures 1nm on an edge a) Calculate the...
Consider an electron in a cubic box that measures 1nm on an edge a) Calculate the energy difference between the ground and first excited states and compare this energy difference with KbT at 300 K. b) Using the Boltzman factor, Nx=N0 exp (-delta E/KbT), calculate and comment on the relative population of the first excited state at this temperature. c) What minimum wavelength is required to excite the electron into the the first excited state d) How would you answer...
Given a 3-dimensional particle-in-a-box system with infinite barriers and L-5nm, Ly-5nm and Li-6n...
Given a 3-dimensional particle-in-a-box system with infinite barriers and L-5nm, Ly-5nm and Li-6nm. Calculate the energies of the ground state and first excited state. List all combinations of values for the quantum numbers nx, ny and nz that are associated with these states.
Given a 3-dimensional particle-in-a-box system with infinite barriers and L-5nm, Ly-5nm and Li-6nm. Calculate the energies of the ground state and first excited state. List all combinations of values for the quantum numbers nx, ny and nz...
3. (a) Consider a 1-dim harmonic oscillator in its ground state (0) of the unperturbed Hamiltonian at t--0o. Let a pert...
3. (a) Consider a 1-dim harmonic oscillator in its ground state (0) of the unperturbed Hamiltonian at t--0o. Let a perturbation Hi(t)--eEXe t2 (e, E and rare constants) be applied between - and too. What is the probability that the oscillator will be in the state n) (of the unperturbed oscillator) as t-> oo?(15%) (b) The bottom of an infinite well is changed to have the shape V(x)-ε sin® for 0Sxa. Calculate the energy shifts for all the excited states...
Huckel/PIB a) Calculate the ground-state energy levels of the π-network in hexatriene, model, and for each...
Huckel/PIB
a) Calculate the ground-state energy levels of the π-network in hexatriene, model, and for each of them indicate the associated degeneracy. To ca molecule is linear and use the values 135 and 154 pm for C-C and C-C bonds CoHs, using the particle in the box lculate the box length, assume that the to induce a transition from the ground state to the first excited e can be obtained using Huckel theory. Knowing b) What is the wavelength of...
The eigenfunctions for a particle in a one-dimensional box of length L, and the corresponding energy eigenvalues are given below. What is the variance of measurements for the linear momentum, i.e., Op = v<p? > - <p>2? Øn (x) = ( )" sin nga, n= 1, 2,.. En = n2h2 8m12 Note the Hamiltonian operator to give the energy is H = = - 42 8n72 dx2 nh 2L oo O nềh2 412 Uncertain since x is known. Following Question...
Particle with a speed bump Consider our old friend the 1D particle in the box, except now with a speed bump in the box so the potential now is given by L and L < x < L 0, Vo 0 x V (x) otherwise (a) Calculate the first order correction to the ground state (n = 1) and first excited state (n = 2) energies (b) Calculate the first order correction to the ground state wave function in terms...
Answer all questions please
5. Consider a particle in the first excited state ofa rigid box of length a. (a) Find the probability density (b) where is the particle most likely to be found? 6. Determine the wavelength of the photon emitted when an electron in a hydrogen atom makes transition from the 5 excited state to the following states (a) ground state (b) 1 excited states (c) 2 excited state Determine whether the emission is visible, uv or infrared...
64 Consider a particle in a one-dimensional box in the ground state v, and the first excited state , described by the wave functions listed below. For each wave function, calculate the expec- tation value of the position (x), the expectation value of the position squared (), the expecta- tion value of the momentum (p), and the expectation value of the momentum squared (p2). 2 . 2x Ossa 0sxSa (b) Y2(x) = Vasin-
1. (50 points) Consider the particle in a one-dimensional box (0 s x S L). Assume a term is added to the Hamiltonian of the form: πχ V(x)g sin Sketch the potential and the expected eigenfunction (small g). In the limit of small g, find the second order correction to the ground state energy 2. (50 points) For a diatomic molecule rotating in free space, the Hamiltonian may be written: 12 21 Where L is the total angular momentum operator,...
8. Consider one electron in a 1D box of side L. Its wavefunction is given by из where ф1(x), фг(x), and фз(x) are the first 3 eigenfunctions of the Hamiltonian, H, of a particle in a 1D box, 2m dx2 a) Is Ψ(x) normalized? If it is not normalized it, normalize it! b) Is Ψ(x) an eigenfunction of A? If it is an eigenfunction, what is the 9. A linear polyene contains 8 -electrons, and absorbs light with412 nm. b)...
Given a 3-dimensional particle-in-a-box system with infinite barriers and L-5nm, Ly-5nm and Li-6nm. Calculate the energies of the ground state and first excited state. List all combinations of values for the quantum numbers nx, ny and nz that are associated with these states.
Given a 3-dimensional particle-in-a-box system with infinite barriers and L-5nm, Ly-5nm and Li-6nm. Calculate the energies of the ground state and first excited state. List all combinations of values for the quantum numbers nx, ny and nz...
3. (a) Consider a 1-dim harmonic oscillator in its ground state (0) of the unperturbed Hamiltonian at t--0o. Let a perturbation Hi(t)--eEXe t2 (e, E and rare constants) be applied between - and too. What is the probability that the oscillator will be in the state n) (of the unperturbed oscillator) as t-> oo?(15%) (b) The bottom of an infinite well is changed to have the shape V(x)-ε sin® for 0Sxa. Calculate the energy shifts for all the excited states...
Huckel/PIB
a) Calculate the ground-state energy levels of the π-network in hexatriene, model, and for each of them indicate the associated degeneracy. To ca molecule is linear and use the values 135 and 154 pm for C-C and C-C bonds CoHs, using the particle in the box lculate the box length, assume that the to induce a transition from the ground state to the first excited e can be obtained using Huckel theory. Knowing b) What is the wavelength of...
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