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- A() An electron is in the spin state x= A Determine the normalisation constant 1...
1-3i An electron is in the spin state x A a. Determine the normalization constant A...
1-3i An electron is in the spin state x A a. Determine the normalization constant A b. Find the expectation value for S c. Find the expectation values for Sx d. Find the expectation values for Sz e. If you measure S on this electron, what values you get, and what is the probability of cachn? f. If you measure on this electron, what values you get, and what is the probability of cachn? g. If you measure Sy on...
An electron is in the spin state x= A () (a) Determine the normalization constant A....
An electron is in the spin state x= A () (a) Determine the normalization constant A. (b) Find the expectation values of Sx , Ŝ, and Ŝ. (c) Find the “uncertainties” Ost, Os, and os, (d) Confirm that your results are consistent with all three uncertainty principles.
4. Spin (10 marks) Suppose an electron is in a state such that its spin can...
4. Spin (10 marks) Suppose an electron is in a state such that its spin can be described by a linear superposition of the eigenspinors of S +A 32 2/22 (a) Normalise the state. (b) What are the possible outcomes of a measurement of the z-component of the spin? What is the probability of each possible result? (c) What are the expectation value and uncertainty of the z-component of the spin? (d) What are the possible results of measuring the...
Consider the state of a spin-1/2 particle 14) = v1o (31+z) + i] – z)) where...
Consider the state of a spin-1/2 particle 14) = v1o (31+z) + i] – z)) where | z) are the eigenstates of the operator of the spin z-component $z. 1. Show that [V) is properly normalized, i.e. (W14) = 1. 2. Calculate the probability that a measurement of $x = 6x yields 3. Calculate the expectation value (Šx) for the state 14) and its dispersion ASx = V(@z) – ($()2. 4. Assume that the spin is placed in the magnetic...
The function ψ2px-1(ψ2,1,1+ψ2,1-1) describes an electron in the 2px state of a hydrogen-like atom (with unspecified...
The function ψ2px-1(ψ2,1,1+ψ2,1-1) describes an electron in the 2px state of a hydrogen-like atom (with unspecified spin). Functions ψη..my are normalized egenfuntions of the energy operator (A), the square of angular momentum operator (12), and the z-component of angular momentum operator (Lz), that is 4. E1 a) Show that the function ψ2px is an eigen function of both the energy operator and the square of angular momentum operator. Find the corresponding eigenvalues. b) Determine the expected value and the uncertainty...
1. Given a state y(r) expanded on the eigenstates of the Hamiltonian for the electron, H, in a hydrogen atom: where the...
1. Given a state y(r) expanded on the eigenstates of the Hamiltonian for the electron, H, in a hydrogen atom: where the subscript of E is n, the principal quantum number. The other two numbers are the 1 and m values, find the expectation values of H (you may use the eigenvalue equation to evaluate for H), L-(total angular momentum operator square), Lz (the z-component of the angular momentum operator) and P (parity operator). Draw schematic pictures of 1 and...
Consider the hydrogen atom and its eigenstates, omitting any effects of fine structure (spin- orb...
Consider the hydrogen atom and its eigenstates, omitting any effects of fine structure (spin- orbit coupling). For the state y21-1 give the a. expectation value of the energy b. c. expectation value of the z-component of the orbital angular momentum d. expectation value of the y-component of the orbital angular momentum e. Now replace the electron with a muon which has a mass mu200 me. What is the ratio expectation value of the total orbital angular momentum of the ground...
[3] A spin-1/2 particle is in the state IW) 1/311) +i2/3|). (a) A measurement is made of the x component of the spi...
[3] A spin-1/2 particle is in the state IW) 1/311) +i2/3|). (a) A measurement is made of the x component of the spin. What is the probability that the spin will be in the +z direction? (b) Suppose a measurement is made of the spin in the z direction and it is found that the particle has m,#1/2. what is the state after the measurement? (c) Now a second measurement is made immediately after to determine the spin in the...
lup)-- CI+) + I-)) I. The spin state: is an eigenvector of one of the ½ spin operators. A) Determine the operator (one...
lup)-- CI+) + I-)) I. The spin state: is an eigenvector of one of the ½ spin operators. A) Determine the operator (one ofs, syor Sz ) of which ly is an eigenvector, and B) determine the corresponding eigenvalue A) spin operator (S Syor S2) for which the above is an eigenvector- B) Eigenvalue- J-s
lup)-- CI+) + I-)) I. The spin state: is an eigenvector of one of the ½ spin operators. A) Determine the operator (one ofs, syor...
3. (a) A particle orbits a fixed point in space. Given that L-=-ih- , find the...
3. (a) A particle orbits a fixed point in space. Given that L-=-ih- , find the eigenvalues аф and normalised eigenfunctions of the z-component of the particle's angular momentum. (5 marks) Explain clearly your reasoning at each important step An electron is in the spin state x)-A G) Normalise x) and hence determine the constant A (ii) If you measured the z-component of the electron's spin, s, . what values could (b) in the usual s basis you get and...
1-3i An electron is in the spin state x A a. Determine the normalization constant A b. Find the expectation value for S c. Find the expectation values for Sx d. Find the expectation values for Sz e. If you measure S on this electron, what values you get, and what is the probability of cachn? f. If you measure on this electron, what values you get, and what is the probability of cachn? g. If you measure Sy on...
An electron is in the spin state x= A () (a) Determine the normalization constant A. (b) Find the expectation values of Sx , Ŝ, and Ŝ. (c) Find the “uncertainties” Ost, Os, and os, (d) Confirm that your results are consistent with all three uncertainty principles.
4. Spin (10 marks) Suppose an electron is in a state such that its spin can be described by a linear superposition of the eigenspinors of S +A 32 2/22 (a) Normalise the state. (b) What are the possible outcomes of a measurement of the z-component of the spin? What is the probability of each possible result? (c) What are the expectation value and uncertainty of the z-component of the spin? (d) What are the possible results of measuring the...
Consider the state of a spin-1/2 particle 14) = v1o (31+z) + i] – z)) where | z) are the eigenstates of the operator of the spin z-component $z. 1. Show that [V) is properly normalized, i.e. (W14) = 1. 2. Calculate the probability that a measurement of $x = 6x yields 3. Calculate the expectation value (Šx) for the state 14) and its dispersion ASx = V(@z) – ($()2. 4. Assume that the spin is placed in the magnetic...
The function ψ2px-1(ψ2,1,1+ψ2,1-1) describes an electron in the 2px state of a hydrogen-like atom (with unspecified spin). Functions ψη..my are normalized egenfuntions of the energy operator (A), the square of angular momentum operator (12), and the z-component of angular momentum operator (Lz), that is 4. E1 a) Show that the function ψ2px is an eigen function of both the energy operator and the square of angular momentum operator. Find the corresponding eigenvalues. b) Determine the expected value and the uncertainty...
1. Given a state y(r) expanded on the eigenstates of the Hamiltonian for the electron, H, in a hydrogen atom: where the subscript of E is n, the principal quantum number. The other two numbers are the 1 and m values, find the expectation values of H (you may use the eigenvalue equation to evaluate for H), L-(total angular momentum operator square), Lz (the z-component of the angular momentum operator) and P (parity operator). Draw schematic pictures of 1 and...
Consider the hydrogen atom and its eigenstates, omitting any effects of fine structure (spin- orbit coupling). For the state y21-1 give the a. expectation value of the energy b. c. expectation value of the z-component of the orbital angular momentum d. expectation value of the y-component of the orbital angular momentum e. Now replace the electron with a muon which has a mass mu200 me. What is the ratio expectation value of the total orbital angular momentum of the ground...
[3] A spin-1/2 particle is in the state IW) 1/311) +i2/3|). (a) A measurement is made of the x component of the spin. What is the probability that the spin will be in the +z direction? (b) Suppose a measurement is made of the spin in the z direction and it is found that the particle has m,#1/2. what is the state after the measurement? (c) Now a second measurement is made immediately after to determine the spin in the...
lup)-- CI+) + I-)) I. The spin state: is an eigenvector of one of the ½ spin operators. A) Determine the operator (one ofs, syor Sz ) of which ly is an eigenvector, and B) determine the corresponding eigenvalue A) spin operator (S Syor S2) for which the above is an eigenvector- B) Eigenvalue- J-s
lup)-- CI+) + I-)) I. The spin state: is an eigenvector of one of the ½ spin operators. A) Determine the operator (one ofs, syor...
3. (a) A particle orbits a fixed point in space. Given that L-=-ih- , find the eigenvalues аф and normalised eigenfunctions of the z-component of the particle's angular momentum. (5 marks) Explain clearly your reasoning at each important step An electron is in the spin state x)-A G) Normalise x) and hence determine the constant A (ii) If you measured the z-component of the electron's spin, s, . what values could (b) in the usual s basis you get and...
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