An infinite square well and a finite square well in 1D with equal width. The potential...
An infinite square well and a finite square well in 1D with equal width. The potential energies of these wells are
Infinite square well: V(x)=0, from 0 < x < a, also V(x) =
, elsewhere
Finite square well: V(x)= 0, from 0 < x < a, also V(x) =
,
elsewhere
The ground state of both systems have identical particles. Without solving the energies of ground states, determine which particle has the higher energy and explain why?
Homework Answers
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An infinite square well and a finite square well in 1D with
equal width. The potential...
Q4. Consider the 1D infinite square-well potential shown in the figure below. V(x) O0 Position (a)...
Q4. Consider the 1D infinite square-well potential shown in the figure below. V(x) O0 Position (a) State the time-independent Schrödinger equation within the region 0<x<L for a particle with positive energy E 2 marks] (b) The wavefunction for 0<x< L can be written in the general form y(x) = Asin kx + B cos kx. Show that the normalised wavefunction for the 1D infinite potential well becomes 2sn'n? ?snT/where ( "1,2,3 ! where ( n = 1,2,5, ). [4 marks]...
For these graphs, they are wave functions of identical particles that are within an infinite square well and their width is a. a.)What is the most probable value of the energy for each wave function...
For these graphs, they are wave functions of identical particles
that are within an infinite square well and their width is a.
a.)What is the most probable value of the energy for each wave
function and which state has the largest probable energy?
b.) Which of these states has the largest expectation value of
the energy? (this part can be done without calculating the
expectation value of the energy)
Vi Aax V2 0 elsewhere elsewhere a x
Vi Aax V2...
The Finite Square Wel A more realistic version of the infinite square well potential has a...
The Finite Square Wel A more realistic version of the infinite square well potential has a finite well depth: -a V(x)--V for -a<x <a for x <-a,'r > a =0 This assignment will consider the bound states of a particle (of mass m) in this potential (i.e. total energy E <0). (1) Determine the general solutions to the time-independent Schrödinger equation for the three regions x <-a, -a<x <a, and > a. Write these solutions in terms of k and...
A NON stationary state A particle of mass m is in an infinite square well potential of width L, a...
A NON stationary state A particle of mass m is in an infinite square well potential of width L, as in McIntyre's section 5.4. Suppose we have an initial state vector lv(t -0) results from Mclntrye without re-deriving them, and you may use a computer for your math as long as you include your code in your solution A(3E1) 4iE2)). You may use E. (4 pts) Use a computer to plot this probability density at 4 times: t 0, t2...
Lcarning Goal: Submit My Answers Glve Up To understand the qualities of the finite square-well potential...
Lcarning Goal: Submit My Answers Glve Up To understand the qualities of the finite square-well potential and how to connect solutions to the Schrödinger equation from different regions. Correct The case of a particle in an infinite potential well, also known as the particle in a box, is one of the simplest in quantum mechanics. The closely related finite potential well is substantially more complicated to solve, but it also shows more of the qualities that are characteristic of quantum...
An electron is trapped in an infinite square-well potential of width 0.3 nm. If the electron...
An electron is trapped in an infinite square-well potential of width 0.3 nm. If the electron is initially in the n = 4 state, what are the various photon energies that can be emitted as the electron jumps to the ground state? (List in descending order of energy. Enter 0 in any remaining unused boxes.) highest eV eV eV eV eV lowest eV
A particle is in the ground state of a symmetric infinite square well with Vx) O...
A particle is in the ground state of a symmetric infinite square well with Vx) O for -a/2<x<+a/2, and infinite elsewhere. (a) The well then undergoes an instantaneous symmetric expansion to -a <<< ta. Calculate the probabilities of the particle being found in each of the three lowest energy states of the larger well. (b) Instead, suppose that the well expansion takes place adiabatically. Again, calculate the probabilities of the particle being found in each of the three lowest energy...
There is a 1-d infinite square well of width a, between x = 0 and a....
There is a 1-d infinite square well of width a, between x = 0 and a. We also know that V(x) = 0 for 0<x<a and +∞ elsewhere. Then we add a perturbation to it so that V(x) = ?_0 for 0 < x < a/2, and the same as before elsewhere. That is, a flat bump of width a/2 and height ?_0 in the left half of the well. Please answer following 3 questions. 1) Sketch the potential and...
Please answer a,b and c. Now, consider a 1-d infinite square well of width a, between...
Please answer a,b and c.
Now, consider a 1-d infinite square well of width a, between x = 0 and a, such that V(x) = 0 for 0<x<a and too elsewhere. A perturbation is then added to it so that V(x) = V. for 0 <x <a/2, and the same as before elsewhere. In other words, a flat bump of width a/2 and height V. in the left half of the well. (a) (5 pts) Carefully sketch the potential and...
X. The first energy correction E) to the 3rd Perturbation of Infinite Square Well. Consider this perturbation to the 1D...
X. The first energy correction E) to the 3rd Perturbation of Infinite Square Well. Consider this perturbation to the 1D infinite square well of width L H1 = eigenenergy E is V(x) A. EL) = EŞV) = V C. EX") " EL) = 1
Q4. Consider the 1D infinite square-well potential shown in the figure below. V(x) O0 Position (a) State the time-independent Schrödinger equation within the region 0<x<L for a particle with positive energy E 2 marks] (b) The wavefunction for 0<x< L can be written in the general form y(x) = Asin kx + B cos kx. Show that the normalised wavefunction for the 1D infinite potential well becomes 2sn'n? ?snT/where ( "1,2,3 ! where ( n = 1,2,5, ). [4 marks]...
For these graphs, they are wave functions of identical particles
that are within an infinite square well and their width is a.
a.)What is the most probable value of the energy for each wave
function and which state has the largest probable energy?
b.) Which of these states has the largest expectation value of
the energy? (this part can be done without calculating the
expectation value of the energy)
Vi Aax V2 0 elsewhere elsewhere a x
Vi Aax V2...
The Finite Square Wel A more realistic version of the infinite square well potential has a finite well depth: -a V(x)--V for -a<x <a for x <-a,'r > a =0 This assignment will consider the bound states of a particle (of mass m) in this potential (i.e. total energy E <0). (1) Determine the general solutions to the time-independent Schrödinger equation for the three regions x <-a, -a<x <a, and > a. Write these solutions in terms of k and...
A NON stationary state A particle of mass m is in an infinite square well potential of width L, as in McIntyre's section 5.4. Suppose we have an initial state vector lv(t -0) results from Mclntrye without re-deriving them, and you may use a computer for your math as long as you include your code in your solution A(3E1) 4iE2)). You may use E. (4 pts) Use a computer to plot this probability density at 4 times: t 0, t2...
Lcarning Goal: Submit My Answers Glve Up To understand the qualities of the finite square-well potential and how to connect solutions to the Schrödinger equation from different regions. Correct The case of a particle in an infinite potential well, also known as the particle in a box, is one of the simplest in quantum mechanics. The closely related finite potential well is substantially more complicated to solve, but it also shows more of the qualities that are characteristic of quantum...
An electron is trapped in an infinite square-well potential of width 0.3 nm. If the electron is initially in the n = 4 state, what are the various photon energies that can be emitted as the electron jumps to the ground state? (List in descending order of energy. Enter 0 in any remaining unused boxes.) highest eV eV eV eV eV lowest eV
A particle is in the ground state of a symmetric infinite square well with Vx) O for -a/2<x<+a/2, and infinite elsewhere. (a) The well then undergoes an instantaneous symmetric expansion to -a <<< ta. Calculate the probabilities of the particle being found in each of the three lowest energy states of the larger well. (b) Instead, suppose that the well expansion takes place adiabatically. Again, calculate the probabilities of the particle being found in each of the three lowest energy...
Please answer a,b and c.
Now, consider a 1-d infinite square well of width a, between x = 0 and a, such that V(x) = 0 for 0<x<a and too elsewhere. A perturbation is then added to it so that V(x) = V. for 0 <x <a/2, and the same as before elsewhere. In other words, a flat bump of width a/2 and height V. in the left half of the well. (a) (5 pts) Carefully sketch the potential and...
X. The first energy correction E) to the 3rd Perturbation of Infinite Square Well. Consider this perturbation to the 1D infinite square well of width L H1 = eigenenergy E is V(x) A. EL) = EŞV) = V C. EX") " EL) = 1
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