Homework Answers
thumbs up please
If you have any doubt regarding this partiular question then please comment
Add Answer to:
Problem 5 The spin raising and lowering operators are define as Su = Sx+iS, and S....
part A is right above part B. Both were uploaded together Write the four vectors S,...
part A is right above part B. Both were uploaded together
Write the four vectors S, S = 1/2,m) (see Problem 21(b)] in terms of , ,) and determine the eigenvalues. (a) J, J2, and J3 are commuting angular momentum operators. Show that the operator § = (ſ* Ì2) İ3, commutes with the total angular momentum j = 31 +32 +33. (This implies that commutes with J? as well.) (b) S1, S2, and S3 are commuting spin-1/2 operators. Let 5,...
1. More on Spin-1/2 system: (10 points) The rising and lowering operators for a spin-1/2 system...
1. More on Spin-1/2 system: (10 points) The rising and lowering operators for a spin-1/2 system are defined as: S+ S + iSy and S S iSy, respectively. They satisfy the following properties: Š+㈩-0, Š+|-)-치+), s-I+) = 최-), s-I-》 = 0, where lt) are the usual eigenstates of the S, operator. a) Invert the definitions of S+ and ś, to express Sa and Šy in terms of St and S. b) Find the matrix representations of Š+ and Š in...
5. Let S-S, + S2 + S, be the total angular momentum of three spin 1/2...
5. Let S-S, + S2 + S, be the total angular momentum of three spin 1/2 particles (whose orbital variables will be ignored). Let | ε1, ε2, ε,' be the eigenstates common to Sla, S2t, ș3s, of respective eigenvalues 1 h/2, e2 h/2, E3ћ/2. Give a basis of eigenvectors common to S2 and S., in terms of the kets Ιει, ε2,E3 Do these two operators form a C.S.C.O.? (Begin by adding two of the spins, then add the partial angular...
Problem #7 The quantum harmonic oscillator Hamiltonian, expressed in terms of raising and lowering operators, is We also know that Using these two statements, show that if then both Yn and ah have we...
Problem #7 The quantum harmonic oscillator Hamiltonian, expressed in terms of raising and lowering operators, is We also know that Using these two statements, show that if then both Yn and ah have well-defined energies. Give these energies in terms of μη.
Problem #7 The quantum harmonic oscillator Hamiltonian, expressed in terms of raising and lowering operators, is We also know that Using these two statements, show that if then both Yn and ah have well-defined energies. Give these energies...
(b) in a direct way Problem #5-20 PTS A spin % system is in the state...
(b) in a direct way Problem #5-20 PTS A spin % system is in the state l) in the usual S2 eigenstate basis IT) - What is the probability that a measurement of Sx yields a value? basis |T) - (a) and | )-(1 2
A spin-1 particle interacts with an external magnetic field B = B. The interaction Hamiltonian for the system is H = gB-S, where S-Si + Sỳ + SE is the spin operator. (Ignore all degrees of freedom ot...
A spin-1 particle interacts with an external magnetic field B = B. The interaction Hamiltonian for the system is H = gB-S, where S-Si + Sỳ + SE is the spin operator. (Ignore all degrees of freedom other than spin.) (a) Find the spin matrices in the basis of the S. S eigenstates, |s, m)) . (Hint: Use the ladder operators, S -S, iS, and S_-S-iS,, and show first that s_ | 1,0-ћ /2 | 1.-1)) . Then use these...
[5] A large number of spin-1/2 particles are run through a Stern-Gerlach machine. When they emerge. all particles have the same spin wave function s)- (where the vector representation is in the...
[5] A large number of spin-1/2 particles are run through a Stern-Gerlach machine. When they emerge. all particles have the same spin wave function s)- (where the vector representation is in the basis set of eigenvectors of Sz. The spin of the particles is measured in the z-direction. On average, 2/3 of the particles have spin in the +z direction and 1/3 in the z direction. (a) Determine one possible normalized spin wave functio tere a single unique solution to...
consider a simple harmonic oscilator and its normalised eigenstates Problem 5. Consider operators B and C,...
consider a simple harmonic oscilator and its normalised
eigenstates
Problem 5. Consider operators B and C, whose matrix representations in some basis are: ſo 10] [1ool 1 0 1 C=o oo Too-1 0 1 0 (a) (10 points) What are the possible values one can obtain if operator C is measured? (b) (10 points) What are the possible states after the measurement? (e) (10) points) Take the state in which C=1. In this state, what are (B) and (BP)? (d)...
5)The residents of S village are raising cattle on public pasture. The cost of feeding a...
5)The residents of S village are raising cattle on public pasture. The cost of feeding a cow is Sb, and the amount and quality of milk produced by a cow will vary according to how much grass the cow can eat on the pasture. When the number of cattle grazing is x, the amount of milk produced by the cattle is vx, and the milk is traded in the market at the price of 1 unit. The individual number of...
1 point) Read 'Diagonalization Changing to a Basis of Eigenvectors' before attempting this problem. Suppose that V is a 5-dimensional vector space. Let S -(vi,... , vs) be some ordered basis...
1 point) Read 'Diagonalization Changing to a Basis of Eigenvectors' before attempting this problem. Suppose that V is a 5-dimensional vector space. Let S -(vi,... , vs) be some ordered basis of V, and let T-(wi.... . ws) be some other ordered basis of V. Let L: V → V be a linear transformation. Let M be the matrix of L in the basis Sand et N be the matrix of L in the basis T. Decide whether each of...
part A is right above part B. Both were uploaded together
Write the four vectors S, S = 1/2,m) (see Problem 21(b)] in terms of , ,) and determine the eigenvalues. (a) J, J2, and J3 are commuting angular momentum operators. Show that the operator § = (ſ* Ì2) İ3, commutes with the total angular momentum j = 31 +32 +33. (This implies that commutes with J? as well.) (b) S1, S2, and S3 are commuting spin-1/2 operators. Let 5,...
1. More on Spin-1/2 system: (10 points) The rising and lowering operators for a spin-1/2 system are defined as: S+ S + iSy and S S iSy, respectively. They satisfy the following properties: Š+㈩-0, Š+|-)-치+), s-I+) = 최-), s-I-》 = 0, where lt) are the usual eigenstates of the S, operator. a) Invert the definitions of S+ and ś, to express Sa and Šy in terms of St and S. b) Find the matrix representations of Š+ and Š in...
5. Let S-S, + S2 + S, be the total angular momentum of three spin 1/2 particles (whose orbital variables will be ignored). Let | ε1, ε2, ε,' be the eigenstates common to Sla, S2t, ș3s, of respective eigenvalues 1 h/2, e2 h/2, E3ћ/2. Give a basis of eigenvectors common to S2 and S., in terms of the kets Ιει, ε2,E3 Do these two operators form a C.S.C.O.? (Begin by adding two of the spins, then add the partial angular...
Problem #7 The quantum harmonic oscillator Hamiltonian, expressed in terms of raising and lowering operators, is We also know that Using these two statements, show that if then both Yn and ah have well-defined energies. Give these energies in terms of μη.
Problem #7 The quantum harmonic oscillator Hamiltonian, expressed in terms of raising and lowering operators, is We also know that Using these two statements, show that if then both Yn and ah have well-defined energies. Give these energies...
(b) in a direct way Problem #5-20 PTS A spin % system is in the state l) in the usual S2 eigenstate basis IT) - What is the probability that a measurement of Sx yields a value? basis |T) - (a) and | )-(1 2
A spin-1 particle interacts with an external magnetic field B = B. The interaction Hamiltonian for the system is H = gB-S, where S-Si + Sỳ + SE is the spin operator. (Ignore all degrees of freedom other than spin.) (a) Find the spin matrices in the basis of the S. S eigenstates, |s, m)) . (Hint: Use the ladder operators, S -S, iS, and S_-S-iS,, and show first that s_ | 1,0-ћ /2 | 1.-1)) . Then use these...
[5] A large number of spin-1/2 particles are run through a Stern-Gerlach machine. When they emerge. all particles have the same spin wave function s)- (where the vector representation is in the basis set of eigenvectors of Sz. The spin of the particles is measured in the z-direction. On average, 2/3 of the particles have spin in the +z direction and 1/3 in the z direction. (a) Determine one possible normalized spin wave functio tere a single unique solution to...
consider a simple harmonic oscilator and its normalised
eigenstates
Problem 5. Consider operators B and C, whose matrix representations in some basis are: ſo 10] [1ool 1 0 1 C=o oo Too-1 0 1 0 (a) (10 points) What are the possible values one can obtain if operator C is measured? (b) (10 points) What are the possible states after the measurement? (e) (10) points) Take the state in which C=1. In this state, what are (B) and (BP)? (d)...
5)The residents of S village are raising cattle on public pasture. The cost of feeding a cow is Sb, and the amount and quality of milk produced by a cow will vary according to how much grass the cow can eat on the pasture. When the number of cattle grazing is x, the amount of milk produced by the cattle is vx, and the milk is traded in the market at the price of 1 unit. The individual number of...
1 point) Read 'Diagonalization Changing to a Basis of Eigenvectors' before attempting this problem. Suppose that V is a 5-dimensional vector space. Let S -(vi,... , vs) be some ordered basis of V, and let T-(wi.... . ws) be some other ordered basis of V. Let L: V → V be a linear transformation. Let M be the matrix of L in the basis Sand et N be the matrix of L in the basis T. Decide whether each of...
Most questions answered within 3 hours.
-
The phylum Protista has often been referred to as a junk drawer
of classification. Explain what...
asked 5 minutes ago -
The average amount of money spent for lunch per person in the
college cafeteria is $7.09...
asked 7 minutes ago -
You follow the lab procedure and at the end of Part 4C, you used
an average...
asked 26 minutes ago -
Write 250-450 words, about the following: • Analyze how a
servant leader in your organization or...
asked 29 minutes ago -
3. American and Japanese workers can each produce 4 cars a
year. An American worker can...
asked 32 minutes ago -
On October 1, 20X1, a company purchased a piece of land by
agreeing to pay the...
asked 45 minutes ago -
Jamie is doing a survey at her school about whether the students
feel the cafeteria food...
asked 50 minutes ago -
What are the roles of 3' and 5' untranslated regions in
mRNAs?
asked 51 minutes ago -
A domestic television receives antenna delivers a sky noise
power of -105 dBm to a matched...
asked 49 minutes ago -
What do you think are the chemical reactions involved in the
breathalyzer tests administered to potentially...
asked 1 hour ago -
A random sample of 120 observations produces a mean of
38.2 from a population with a...
asked 1 hour ago -
The average area of land burned by forest fires every year in
Canada is 2.5 million...
asked 1 hour ago