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1-3i 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....
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.
- A() An electron is in the spin state x= A Determine the normalisation constant 1...
- A() An electron is in the spin state x= A Determine the normalisation constant 1 i A, and then find the expectation value of the z-component of the spin operator h [6]
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...
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...
The Cartesian components Sx, Sy, and Sz, of spin satisfy the commutation relation [Sx, Sy] =...
The Cartesian components Sx, Sy, and Sz, of spin satisfy the commutation relation [Sx, Sy] = ihsz Measurements of Sy are performed on an ensemble of systems prepared in the state given by 14 ) = (3+i) I+) + (1 + 5i) |-) where =) are the Sy eigenkets v. Give the possible outcomes of an Sx measurement and the probability for each outcome. vi. Determine the exact uncertainty Osz in Sy and compare with the smallest value it can...
[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...
1 2. Consider the normalized spin state To (31t) +i\L)) (2) 10 (a) Is this state...
1 2. Consider the normalized spin state To (31t) +i\L)) (2) 10 (a) Is this state lx) an eigenstate of $2 ? Is it an eigenstate of Ŝe ? (Justify your answers.) In each case, if it is an eigenstate, give the eigenvalue. (b) If the spin state is as given above, and a measurement is made of the 2-component of the angular momentum, what are the possible results of that measurement and what are probabilities of each possible result?...
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...
Please solve question 3 ,4,5,6 the state IL,tni is an eigenvestor of i and izg with...
Please solve question 3 ,4,5,6
the state IL,tni is an eigenvestor of i and izg with eigeanvalues of +1) and mzh, respectively. Find L>and<I2> n electron is placed in a uniform magnetic field B Bok. At time t O S, was measured and was found to be h/2. (a) (5 points) Write its spin wavefunction at any later time t. (b) (5 points) Calculate < S () (5 pointa) At what time t if you mensure the y component of...
3- A one-dimensional harmonic oscillator wave function is ψ(x) = Axe-bx2 a) Find the total energy...
3- A one-dimensional harmonic oscillator wave function is ψ(x) = Axe-bx2 a) Find the total energy E b) Find the constant b c) Find the normalization constant A. d) Find the expectation value of x, e) Find the uncertainty in x, Ох. f) Find the expectation value of p g) Find the uncertainty in p, Op For the Hamiltonian matrix shown below:
3- A one-dimensional harmonic oscillator wave function is ψ(x) = Axe-bx2 a) Find the total energy E b)...
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.
- A() An electron is in the spin state x= A Determine the normalisation constant 1 i A, and then find the expectation value of the z-component of the spin operator h [6]
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...
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...
The Cartesian components Sx, Sy, and Sz, of spin satisfy the commutation relation [Sx, Sy] = ihsz Measurements of Sy are performed on an ensemble of systems prepared in the state given by 14 ) = (3+i) I+) + (1 + 5i) |-) where =) are the Sy eigenkets v. Give the possible outcomes of an Sx measurement and the probability for each outcome. vi. Determine the exact uncertainty Osz in Sy and compare with the smallest value it can...
[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...
1 2. Consider the normalized spin state To (31t) +i\L)) (2) 10 (a) Is this state lx) an eigenstate of $2 ? Is it an eigenstate of Ŝe ? (Justify your answers.) In each case, if it is an eigenstate, give the eigenvalue. (b) If the spin state is as given above, and a measurement is made of the 2-component of the angular momentum, what are the possible results of that measurement and what are probabilities of each possible result?...
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...
Please solve question 3 ,4,5,6
the state IL,tni is an eigenvestor of i and izg with eigeanvalues of +1) and mzh, respectively. Find L>and<I2> n electron is placed in a uniform magnetic field B Bok. At time t O S, was measured and was found to be h/2. (a) (5 points) Write its spin wavefunction at any later time t. (b) (5 points) Calculate < S () (5 pointa) At what time t if you mensure the y component of...
3- A one-dimensional harmonic oscillator wave function is ψ(x) = Axe-bx2 a) Find the total energy E b) Find the constant b c) Find the normalization constant A. d) Find the expectation value of x, e) Find the uncertainty in x, Ох. f) Find the expectation value of p g) Find the uncertainty in p, Op For the Hamiltonian matrix shown below:
3- A one-dimensional harmonic oscillator wave function is ψ(x) = Axe-bx2 a) Find the total energy E b)...
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