Homework Answers
1. C.
2. E
3. I cant see the Figure B
please find the explaimations in the below image
we
solve the co-efficents by boundry conditions that wave function
must be continous, differential every where and noramilizied
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Consider a finite square barrier potential shown below. Figure A. For a<x<b, the space part of...
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...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width L represented by a step function ſo I<0 or 1>L V U. r>0 and 2<L The total wavefunction is subject to the time-independent Schrödinger equation = EV (2) 2m ar2 +V where E is the energy of the quantum particle in question and m is the mass of the quantum particle. A The total wavefunction of a free particle that enters the barrier from...
Consider a particle of mass in a 10 finite potential well of height V. the domain...
Consider a particle of mass in a 10 finite potential well of height V. the domain – a < x < a. a) Show that solutions for – a < x < a take the form on (x) = A cos(knx) for odd n, and on (x) = A sin(knx) for even n. . Show a) Match the boundary conditions at x = a to prove that cos(ka) = Bk where k is the wave vector for -a < x...
mechani mie The potential energy barrier shown below is a simplified model of thec electrons in...
mechani mie The potential energy barrier shown below is a simplified model of thec electrons in metals. The metal workfunction (Ew), the minimum energy required to remove an electron from the metal, is given by Ew-,-E where 1s the height of the potential energy barrier and E is the energy of the electrons near the surface of the metal. The potential energy barrier is = 5 eV V(x) V=0 (a) The wavefunction of an electron on the surface (x< 0)...
5. Consider a square potential barrier in figure below: V(x) 0 x <0 a) Assume that...
5. Consider a square potential barrier in figure below: V(x) 0 x <0 a) Assume that incident particles of energy E> v are coming from-X. Find the stationary states (the equations for region . 2 and 3 and the main equation for the all regions). Apply the matching limit conditions in the figure. Explain and find all the constants used in the equations in terms of the parameters provided and Planck's constant -(6) Find the transmission and reflection coefficients. -(4)
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...
Figure show finite non-square well and bound energy level shown there. U(X) Total energy of the...
Figure show finite non-square well and bound energy level shown there. U(X) Total energy of the particle a) Plot qualitatively, square finite well wave function of 4th state. b) Plot qualitatively, non-square well shown here 4h state again. c) Show most probable place of an electron on your plot.
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]...
[Finite potential well] Consider a symmetric square well potential of a finite depth, i.e., V(x) =...
[Finite potential well] Consider a symmetric square well potential of a finite depth, i.e., V(x) = 0 inside the well, V(x) = V outside the well. NOTE: for a general discontinuous potential the boundary conditions are the continuity of both the wave function and its first derivative at the point(s) of the discontinuity of the potential y (x_)=y(x),y'(x_)=y'(x4) (i) What are the functional forms of the solutions for y(x) inside and outside the well? (ii) What are the explicit continuity...
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...
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...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width L represented by a step function ſo I<0 or 1>L V U. r>0 and 2<L The total wavefunction is subject to the time-independent Schrödinger equation = EV (2) 2m ar2 +V where E is the energy of the quantum particle in question and m is the mass of the quantum particle. A The total wavefunction of a free particle that enters the barrier from...
Consider a particle of mass in a 10 finite potential well of height V. the domain – a < x < a. a) Show that solutions for – a < x < a take the form on (x) = A cos(knx) for odd n, and on (x) = A sin(knx) for even n. . Show a) Match the boundary conditions at x = a to prove that cos(ka) = Bk where k is the wave vector for -a < x...
mechani mie The potential energy barrier shown below is a simplified model of thec electrons in metals. The metal workfunction (Ew), the minimum energy required to remove an electron from the metal, is given by Ew-,-E where 1s the height of the potential energy barrier and E is the energy of the electrons near the surface of the metal. The potential energy barrier is = 5 eV V(x) V=0 (a) The wavefunction of an electron on the surface (x< 0)...
5. Consider a square potential barrier in figure below: V(x) 0 x <0 a) Assume that incident particles of energy E> v are coming from-X. Find the stationary states (the equations for region . 2 and 3 and the main equation for the all regions). Apply the matching limit conditions in the figure. Explain and find all the constants used in the equations in terms of the parameters provided and Planck's constant -(6) Find the transmission and reflection coefficients. -(4)
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...
Figure show finite non-square well and bound energy level shown there. U(X) Total energy of the particle a) Plot qualitatively, square finite well wave function of 4th state. b) Plot qualitatively, non-square well shown here 4h state again. c) Show most probable place of an electron on your plot.
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]...
[Finite potential well] Consider a symmetric square well potential of a finite depth, i.e., V(x) = 0 inside the well, V(x) = V outside the well. NOTE: for a general discontinuous potential the boundary conditions are the continuity of both the wave function and its first derivative at the point(s) of the discontinuity of the potential y (x_)=y(x),y'(x_)=y'(x4) (i) What are the functional forms of the solutions for y(x) inside and outside the well? (ii) What are the explicit continuity...
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...
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