Homework Answers
Add Answer to:
3. Using position and momentum operators prove that <xp>
= -<px> = ihbar/2 for the infinite...
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]...
3 Angular Momentum and Spherical Harmonics For a quantum mechanical system that is able to rotate...
3 Angular Momentum and Spherical Harmonics For a quantum mechanical system that is able to rotate in 3D, one can always define a set of angular momentum operators J. Jy, J., often collectively written as a vector J. They must satisfy the commutation relations (, ] = ihſ, , Îu] = ihſ, J., ſu] = ihỈy. (1) In a more condensed notation, we may write [1,1]] = Žiheikh, i, j= 1,2,3 k=1 Here we've used the Levi-Civita symbol, defined as...
Question 8 please 5. We start with Schrodinger's Equation in 2(x,t) = H¥(x,t). We can write...
Question 8 please
5. We start with Schrodinger's Equation in 2(x,t) = H¥(x,t). We can write the time derivative as 2.4(x, t) = V(x,+) - (xt), where At is a sufficiently small increment of time. Plug the algebraic form of the derivative into Schrodinger's Eq. and solve for '(x,t+At). b. Put your answer in the form (x,t+At) = T '(x,t). c. What physically does the operator T do to the function '(x,t)? d. Deduce an expression for '(x,t+24t), in terms...
Parity (please answer from part a to part d) Consider Infinite Square Well Potential, V(x) =...
Parity (please answer from part a to part d)
Consider Infinite Square Well Potential,
V(x) = 0 for |x| < 1/2a and V(x) = infinity for |x| >
1/2a
a) Find energy eigenstates and eigenvalues by solving eigenvalue
equation using appropriate boundary conditions. And show
orthogonality of eigenstates.
For rest of part b to part d please look at the image below:
Problem 1 . Parity Consider an infinite square well potential, V(x) = 0 for lxl 〈 a and...
7 Harmonic oscillator in "energy space" Consider the harmonic oscillator in "energy space", i.e., in terms...
7 Harmonic oscillator in "energy space" Consider the harmonic oscillator in "energy space", i.e., in terms of the basis of eigenvectors n) of the harmonic oscillator Hamiltonian, with Hn) -hwn1/2)]n). We computed these in terms of wavefunctions in position space, ie. pn(x)-(zln), but we can also work purely in terms of the abstract energy eigenvectors in Dirac notation. PS9.pdf 1. You computed the matrix elements 〈nleln) on an earlier problem set. Now find (nn) for general n,n' 2. Find the...
(15 points) Encounter with a semi-infinite potential "well" In this problem we will investigate one situation involving a a semi-infinite one-dimensional po- tential well (Figure 1) U=0 regio...
(15 points) Encounter with a semi-infinite potential "well" In this problem we will investigate one situation involving a a semi-infinite one-dimensional po- tential well (Figure 1) U=0 region 1 region 2 region 3 Figure 1: Semi-infinite potential for Problem 3 This potential is piecewise defined as follows where Uo is some positive value of energy. The three intervals in x have been labeled region 1,2 and 3 in Figure 1 Consider a particle of mass m f 0 moving in...
Please help with computer science Consider the following truth table, where X, Y, and Z are...
Please help with computer science Consider the following truth table, where X, Y, and Z are Boolean variable inputs and W is a Boolean-valued result: X Y Z W 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 Write an expression for the above table using ~&|. Consider the following truth table, where X, Y, and Z...
qm 09.3 3. An operator  is Hermitian if it satisfies the condition $ $(y) dx...
qm 09.3
3. An operator  is Hermitian if it satisfies the condition $ $(y) dx = (Ap) u dx, for any wavefunctions $(x) and y(x). (i) The time dependent Schrödinger equation is ih au = fu, at where the Hamiltonian operator is Hermitian. Show that the equation of mo- tion for the expectation value of any Hermitian operator  is given by d(A) IH, Â]), dt ħi i = where the operator  does not depend explicitly on time....
3 At a given time, the normalised wave function for a particle in a one-dimensional infinite...
3 At a given time, the normalised wave function for a particle in a one-dimensional infinite square well -a < x < a is given by 2 sin2 V inside the well and zero outside. Find the probability that a measurement of energy yields the eigenvalue En. (Hint: use data on page 6.) [6] Useful Data and Formulas = 1.60 x 10-19 C Elementary charge e h/2T=1.05 x 10-34 Js Planck's constant 3.00 x 108 m s-1 Speed of light...
Consider an infinite sequence of positions 1, 2, 3, . . . and suppose we have a stone at position 1 and another stone at position 2. In each step, we choose one of the stones and move it according to...
Consider an infinite sequence of positions 1, 2, 3, . . . and suppose we have a stone at position 1 and another stone at position 2. In each step, we choose one of the stones and move it according to the following rule: Say we decide to move the stone at position i; if the other stone is not at any of the positions i + 1, i + 2, . . . , 2i, then it goes to...
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]...
3 Angular Momentum and Spherical Harmonics For a quantum mechanical system that is able to rotate in 3D, one can always define a set of angular momentum operators J. Jy, J., often collectively written as a vector J. They must satisfy the commutation relations (, ] = ihſ, , Îu] = ihſ, J., ſu] = ihỈy. (1) In a more condensed notation, we may write [1,1]] = Žiheikh, i, j= 1,2,3 k=1 Here we've used the Levi-Civita symbol, defined as...
Question 8 please
5. We start with Schrodinger's Equation in 2(x,t) = H¥(x,t). We can write the time derivative as 2.4(x, t) = V(x,+) - (xt), where At is a sufficiently small increment of time. Plug the algebraic form of the derivative into Schrodinger's Eq. and solve for '(x,t+At). b. Put your answer in the form (x,t+At) = T '(x,t). c. What physically does the operator T do to the function '(x,t)? d. Deduce an expression for '(x,t+24t), in terms...
Parity (please answer from part a to part d)
Consider Infinite Square Well Potential,
V(x) = 0 for |x| < 1/2a and V(x) = infinity for |x| >
1/2a
a) Find energy eigenstates and eigenvalues by solving eigenvalue
equation using appropriate boundary conditions. And show
orthogonality of eigenstates.
For rest of part b to part d please look at the image below:
Problem 1 . Parity Consider an infinite square well potential, V(x) = 0 for lxl 〈 a and...
7 Harmonic oscillator in "energy space" Consider the harmonic oscillator in "energy space", i.e., in terms of the basis of eigenvectors n) of the harmonic oscillator Hamiltonian, with Hn) -hwn1/2)]n). We computed these in terms of wavefunctions in position space, ie. pn(x)-(zln), but we can also work purely in terms of the abstract energy eigenvectors in Dirac notation. PS9.pdf 1. You computed the matrix elements 〈nleln) on an earlier problem set. Now find (nn) for general n,n' 2. Find the...
(15 points) Encounter with a semi-infinite potential "well" In this problem we will investigate one situation involving a a semi-infinite one-dimensional po- tential well (Figure 1) U=0 region 1 region 2 region 3 Figure 1: Semi-infinite potential for Problem 3 This potential is piecewise defined as follows where Uo is some positive value of energy. The three intervals in x have been labeled region 1,2 and 3 in Figure 1 Consider a particle of mass m f 0 moving in...
qm 09.3
3. An operator  is Hermitian if it satisfies the condition $ $(y) dx = (Ap) u dx, for any wavefunctions $(x) and y(x). (i) The time dependent Schrödinger equation is ih au = fu, at where the Hamiltonian operator is Hermitian. Show that the equation of mo- tion for the expectation value of any Hermitian operator  is given by d(A) IH, Â]), dt ħi i = where the operator  does not depend explicitly on time....
3 At a given time, the normalised wave function for a particle in a one-dimensional infinite square well -a < x < a is given by 2 sin2 V inside the well and zero outside. Find the probability that a measurement of energy yields the eigenvalue En. (Hint: use data on page 6.) [6] Useful Data and Formulas = 1.60 x 10-19 C Elementary charge e h/2T=1.05 x 10-34 Js Planck's constant 3.00 x 108 m s-1 Speed of light...
Most questions answered within 3 hours.
-
accorsing to the data from thw college board, the mean wuantitive
Sat score for s demale...
asked 53 minutes ago -
1- What are 5 general characteristics of Botticelli’s
paintings?
2- Describe 5 important traits of Flemish...
asked 2 hours ago -
A golfer claims that his average golf score at the course he
plays regularly is less...
asked 3 hours ago -
On May 1, First Bank perfected a security interest in Debtor’s
inventory. On June 1, Bob...
asked 3 hours ago -
A new kind of typhoid shot is being developed by a medical
research team. The old...
asked 5 hours ago -
Write a chemical equation for these reactions. (Use
the lowest possible whole number coefficients.) Include
states-of-matter...
asked 7 hours ago -
For each of the Z-scores below, determine two probabilities
(show four three decimal places): (1) the...
asked 7 hours ago -
Oxidative phosphorylation is achieved through chemiosmotic
coupling, which turns chemical energy into osmotic potential energy
that...
asked 10 hours ago -
Hollywood Shoes would like to maintain their cash account at a
minimum level of $64,000, but...
asked 10 hours ago -
Proteins CtrA-P, DnaA, and GcrA behave similarly to what
molecule in the Eukaryotic Cell Cycle?
asked 10 hours ago -
TRUE OR FALSE
In case of a competitive tender procedure, in the request for
quotation, the...
asked 10 hours ago -
I am a little behind please provide some explanation, will
provide thumbs up.
This question considers...
asked 10 hours ago