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. A particle is subject to the potential shown below: v (x) 5 V(x)-k2, when 0...
3.9. A particle of mass m is confined in the potential well 0 0<x < L...
3.9. A particle of mass m is confined in the potential well 0 0<x < L oo elsewhere (a) At time t 0, the wave function for the particle is the one given in Problem 3.3. Calculate the probability that a measurement of the energy yields the value En, one of the allowed energies for a particle in the box. What are the numerical values for the probabilities of obtaining the ground-state energy E1 and the first-excited-state energy E2? Note:...
Find the energy eigenvalues of a particle confined by a potential of the following form: +oo,...
Find the energy eigenvalues of a particle confined by a potential of the following form: +oo, V(r)= { }mu22, if 2 0. if r0 < Sketch the potential so that you have a visual picture of it. Hint: Use the fact that we already know the energy eigenvalues and eigenfunctions of the Schrödi- inger equation in the quadratic potential and impose an additional requirement to the wave func- tions that follows from V(r) = 0. o for
1) A particle with mass m moves under the influence of a potential field . The...
1) A particle with mass m moves under the influence of a
potential field . The
particle wave function is stated by:
for
where and
are
constants.
(a) Show that is not time
dependent.
(b) Determine as the
normalization constant.
(c) Calculate the energy and momentum of the particle.
(d) Show that
V (x /km/2h+it/k/m Aar exp (ar, t) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable...
Consider a particle incident from the left on the potential step. Where E = 2 eV...
Consider a particle incident from the left on the potential step. Where E = 2 eV V(x) {5 eV lo x < 0 x > 0 1) Find the wave function of the particle in two regions 2) Find reflection and transmission coefficients R and T
Consider a particle in a 1-dimensional ininite square well potential {0, V(z)=Í oo, (-a < z...
Consider a particle in a 1-dimensional ininite square well potential {0, V(z)=Í oo, (-a < z <a) elsewhere The particle is initially localized in the right side of the well (O S a) Calculate the probability that at later times, an energy measurement will yield the energy of the first excited state of this system
Hello, please help with this problem. Thanks in advance. 3. Consider a step potential shown in...
Hello, please help with this problem. Thanks in
advance.
3. Consider a step potential shown in Figure B. Which of the following statement is correct for a particle with E<0. (a) The form of the wave function to the left is elk, where k2 = 2mE/h?. (b) The form of the wave function to the left is eiex where g?=2m(V.-E)/h. (d) All of the above. (e) None of the above. 4- If the particle energy E was 0<E<V. for the...
Consider a particle in a 1-d well with potential V(x) =-U for-d < x < d,...
Consider a particle in a 1-d well with potential V(x) =-U for-d < x < d, and V(z) 0 elsewhere. We will use the variational wave function v(z) = A(b + r), t(x)-A(b-x), -b < r < 0, 0 < x < b, to show that a bound state exists for any U0. a) Normalize the wave function. Find the expectation values of the kinetic and potential energies b) Show that for sufficiently large b, with b> d, the expectation...
Consider a particle of mass m moving in a one-dimensional potential of the form V. for...
Consider a particle of mass m moving in a one-dimensional potential of the form V. for 0<x<b, V(a) = 0 for Islal<e, for 1212, with V., b and c positive constants and c>b. a Explain why the wave function of the particle can be assumed to be cither an even function or an odd function of a. b For the case that the energy E of the particle is in the range 0<ESV., find the (unnormalized) even cigenfunctions and give...
Question 2: A particle of mass m moves in a potential energy U(x) that is zero...
Question 2: A particle of mass m moves in a potential energy U(x) that is zero forェ* 0 and is-oo at r-0. This is am attractive delta function, very odd. Do not worry about the physical meaning of the potential, just roll with it for now. The system is described by the wave function Afor <0 where a is a real, positive constant with dimensions of 1/Length, and A is the normalization constant, treat it as a unknown complex-number for...
Consider a finite square barrier potential shown below. Figure A. For a<x<b, the space part of...
Consider a finite square barrier potential shown below. Figure A. For a<x<b, the space part of the electron wave function has the form: k? = 2mE/h? and gu2m(V,-E)/h2 (a) Aeikx (b) Aegn (c) Ae*** + Be** (d) Ae* (e) Aelkx + Be-ika For the finite square barrier potential shown below, Figure A. For x<a, the space part of the electron wave function has the form: k = 2mE/h? and g=2m(Vo-E) /h (a) Aeikx (b) Aetex (c) Ae*EN + Bet* (d)...
3.9. A particle of mass m is confined in the potential well 0 0<x < L oo elsewhere (a) At time t 0, the wave function for the particle is the one given in Problem 3.3. Calculate the probability that a measurement of the energy yields the value En, one of the allowed energies for a particle in the box. What are the numerical values for the probabilities of obtaining the ground-state energy E1 and the first-excited-state energy E2? Note:...
Find the energy eigenvalues of a particle confined by a potential of the following form: +oo, V(r)= { }mu22, if 2 0. if r0 < Sketch the potential so that you have a visual picture of it. Hint: Use the fact that we already know the energy eigenvalues and eigenfunctions of the Schrödi- inger equation in the quadratic potential and impose an additional requirement to the wave func- tions that follows from V(r) = 0. o for
1) A particle with mass m moves under the influence of a
potential field . The
particle wave function is stated by:
for
where and
are
constants.
(a) Show that is not time
dependent.
(b) Determine as the
normalization constant.
(c) Calculate the energy and momentum of the particle.
(d) Show that
V (x /km/2h+it/k/m Aar exp (ar, t) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable...
Consider a particle incident from the left on the potential step. Where E = 2 eV V(x) {5 eV lo x < 0 x > 0 1) Find the wave function of the particle in two regions 2) Find reflection and transmission coefficients R and T
Consider a particle in a 1-dimensional ininite square well potential {0, V(z)=Í oo, (-a < z <a) elsewhere The particle is initially localized in the right side of the well (O S a) Calculate the probability that at later times, an energy measurement will yield the energy of the first excited state of this system
Hello, please help with this problem. Thanks in
advance.
3. Consider a step potential shown in Figure B. Which of the following statement is correct for a particle with E<0. (a) The form of the wave function to the left is elk, where k2 = 2mE/h?. (b) The form of the wave function to the left is eiex where g?=2m(V.-E)/h. (d) All of the above. (e) None of the above. 4- If the particle energy E was 0<E<V. for the...
Consider a particle in a 1-d well with potential V(x) =-U for-d < x < d, and V(z) 0 elsewhere. We will use the variational wave function v(z) = A(b + r), t(x)-A(b-x), -b < r < 0, 0 < x < b, to show that a bound state exists for any U0. a) Normalize the wave function. Find the expectation values of the kinetic and potential energies b) Show that for sufficiently large b, with b> d, the expectation...
Consider a particle of mass m moving in a one-dimensional potential of the form V. for 0<x<b, V(a) = 0 for Islal<e, for 1212, with V., b and c positive constants and c>b. a Explain why the wave function of the particle can be assumed to be cither an even function or an odd function of a. b For the case that the energy E of the particle is in the range 0<ESV., find the (unnormalized) even cigenfunctions and give...
Question 2: A particle of mass m moves in a potential energy U(x) that is zero forェ* 0 and is-oo at r-0. This is am attractive delta function, very odd. Do not worry about the physical meaning of the potential, just roll with it for now. The system is described by the wave function Afor <0 where a is a real, positive constant with dimensions of 1/Length, and A is the normalization constant, treat it as a unknown complex-number for...
Consider a finite square barrier potential shown below. Figure A. For a<x<b, the space part of the electron wave function has the form: k? = 2mE/h? and gu2m(V,-E)/h2 (a) Aeikx (b) Aegn (c) Ae*** + Be** (d) Ae* (e) Aelkx + Be-ika For the finite square barrier potential shown below, Figure A. For x<a, the space part of the electron wave function has the form: k = 2mE/h? and g=2m(Vo-E) /h (a) Aeikx (b) Aetex (c) Ae*EN + Bet* (d)...
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