A particle on a sphere is described by the state function Ψ = N {1 +...
A particle on a sphere is described by the state function Ψ = N {1 + cos(θ)}
Find
a) the value of the normalization constant N
b) the expectation value of the energy E
c) the possible values of the z component of angular momentum (Lz) that might be measured, and which of these possibilities is most likely.
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A particle on a sphere is described by the state function Ψ = N
{1 +...
Question #2: 6 pts] Find the eigenvalues and the normalized eigenvectors of the matrix 21 2...
Question #2: 6 pts] Find the eigenvalues and the normalized eigenvectors of the matrix 21 2 -1 2 Question #3: 10 pts] The electron in a hydrogen atom is a linear combination of eigenstates. Let us assume a limited linear combination to provide some sample calculations $(r, θ, φ) 2 ,1,0,0 + '2,1,0 (a) Normalize the above equation. (b) What are the possible results of individual measurements of energy, angular momentum, and the z-component of angular momentum? (c) What are...
##### show all steps thoroughly (sorry for my bad grammar) Assume that electron in area electric field of proton and in the state wave function r + 2p2 1,0.0 1) Find expectation value of energy 2) Fi...
##### show all steps thoroughly (sorry for my bad grammar)
Assume that electron in area electric field of proton and in the state wave function r + 2p2 1,0.0 1) Find expectation value of energy 2) Find expectation value of angular momentum squared (L2) 3) Find expectation value of angular momentum in component axis -Z L) 4) How much angular momentum in component axis-Z will probability of found particle? And why?
Assume that electron in area electric field of proton...
A particle moves in an infnite potential well described by V(r) o, l> a/2. are of...
A particle moves in an infnite potential well described by V(r) o, l> a/2. are of the forn vn (z)-A" cos (k,,e), or Un(r) B," sin (knz), depending on the value of n. For n 3, (r)-(V2/a) cos (3Tr/a) for lrl S a/2 and var t are the expectation values of r and a2 in the n 3 state. ) What are the expectation values of p and p2 in the n-3 state. To calculate the expectation value for momentum,...
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A hydrogen atom is in the n = 6 state. Determine, according to quantum mechanics, (a) the total energy (in eV) of the atom, (b) the magnitude of the maximum angular momentum the electron can have in this state, and (c) the maximum value that the z component Lz of the angular momentum can have.
A particle moves in an infinite potential well described by The eigenfunctions are of the form...
A particle moves in an infinite potential well described by The eigenfunctions are of the form (r) = A For n = 3. e3(r) = (v/2/n) cos(3mr/n) for lrl cos (knr), or er (r) = Dn sin (k, r), depending E0 for o/2 and t's(r)- (a) What are the expectation values of r and 2 in the n 3 state. (b) What are the expectation values of p and p2 in the n 3 state. To calculate the expectation value...
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...
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...
(V.4) A particle is observed to have orbital angular momentum quantum number 2. The z component...
(V.4) A particle is observed to have orbital angular momentum quantum number 2. The z component of the angular momentum is measured to be Lz2h. A second particle is observed to have orbital angular momentum quantum number l2-2 and a z component ha = +2 V1(1 +1), what are the possible outcomes, and with what relative probabilities? What is the expectation value (L)'? h. If a measurement is made of the total angular momentum L-h
1: For a free particle, U(x)-0, in the state Ψ(x)-e®, determine if the particle is in...
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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...
Question #2: 6 pts] Find the eigenvalues and the normalized eigenvectors of the matrix 21 2 -1 2 Question #3: 10 pts] The electron in a hydrogen atom is a linear combination of eigenstates. Let us assume a limited linear combination to provide some sample calculations $(r, θ, φ) 2 ,1,0,0 + '2,1,0 (a) Normalize the above equation. (b) What are the possible results of individual measurements of energy, angular momentum, and the z-component of angular momentum? (c) What are...
##### show all steps thoroughly (sorry for my bad grammar)
Assume that electron in area electric field of proton and in the state wave function r + 2p2 1,0.0 1) Find expectation value of energy 2) Find expectation value of angular momentum squared (L2) 3) Find expectation value of angular momentum in component axis -Z L) 4) How much angular momentum in component axis-Z will probability of found particle? And why?
Assume that electron in area electric field of proton...
A particle moves in an infnite potential well described by V(r) o, l> a/2. are of the forn vn (z)-A" cos (k,,e), or Un(r) B," sin (knz), depending on the value of n. For n 3, (r)-(V2/a) cos (3Tr/a) for lrl S a/2 and var t are the expectation values of r and a2 in the n 3 state. ) What are the expectation values of p and p2 in the n-3 state. To calculate the expectation value for momentum,...
A particle moves in an infinite potential well described by The eigenfunctions are of the form (r) = A For n = 3. e3(r) = (v/2/n) cos(3mr/n) for lrl cos (knr), or er (r) = Dn sin (k, r), depending E0 for o/2 and t's(r)- (a) What are the expectation values of r and 2 in the n 3 state. (b) What are the expectation values of p and p2 in the n 3 state. To calculate the expectation value...
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...
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...
(V.4) A particle is observed to have orbital angular momentum quantum number 2. The z component of the angular momentum is measured to be Lz2h. A second particle is observed to have orbital angular momentum quantum number l2-2 and a z component ha = +2 V1(1 +1), what are the possible outcomes, and with what relative probabilities? What is the expectation value (L)'? h. If a measurement is made of the total angular momentum L-h
1: For a free particle, U(x)-0, in the state Ψ(x)-e®, determine if the particle is in an eigenstate of the following operators and give the eigenvalue if it is. a position z m b. momentum c. Energy d. Translation (D)
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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