. What behaviors indicate psychological distress? Name 5 and explain.

## . What behaviors indicate psychological distress? Name 5 and explain.

The term ‘distress’ is commonly used in nursing literature to … Read More...
13-In a criminal case, the state must prove its case by a preponderance of the evidence. True False

## 13-In a criminal case, the state must prove its case by a preponderance of the evidence. True False

13-In a criminal case, the state must prove its case … Read More...
Prove that cosx=1-tan^2 x/2 / 1+tan^2 x/2

## Prove that cosx=1-tan^2 x/2 / 1+tan^2 x/2

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Course: PHYS 5426 — Quantum Statistical Physics Assignment #1 Instructor: Gennady Y. Chitov Date Assigned: January 15, 2014 Due Date: January 29, 2014 Problem 1. Prove [a; f(a†)] = @f(a†) @a† (1) [a†; f(a)] = −@f(a) @a (2) for arbitrary function f of operator which admits a series expansion. The Bose creation/ annihilation operators satisfy the standard commutation relations [a; a†] ≡ aa† − a†a = 1 (3) Hint: From Eqs.(1,2) one can figure out the corresponding commutation relations for the powers of creation/annihilation operators and then prove them by the method of mathematical induction. Note that for an arbitrary operator Aˆ: @A^n @A^ = nAˆn−1. Problem 2. In the presence of a constant external force acting on a one-dimensional oscillating particle its Hamiltonian becomes that of the so-called displaced oscillator, and the Schr¨odinger equation ˆH (q) = E (q) of the problem (cf. lecture notes) can be written in terms of dimensionless variables as ( − 1 2 d2 d2 + 1 2 2 − √ 2  ) () = ” () ; (4) where q = √ ~ m! and E = ~!”. a). Write the Schr¨odinger equation (4) in terms of the creation/annihilation operators of the harmonic oscillator ( = 0)  = √1 2 (a + a†) (5) d d = √1 2 (a − a†) (6) 1 Via a linear transformation to the new creation/annihilation operators ˜a†; ˜a preserving the bosonic commutation relations for ˜a†; ˜a map the problem (4) of the displaced oscillator onto that of a simple harmonic oscillator with new operators (˜a†; ˜a). b). Find the spectrum (eigenvalues) ” (E) of the displaced oscillator. c). Write the normalized eigenstates |n⟩ of the displaced Hamiltonian (4) via a† and the vacuum state |Θ◦⟩ of the new operators, i.e. ˜a|Θ◦⟩ = 0 (7) d). As follows from the completeness of the oscillator’s eigenstates, the vacuum state of the displaced oscillator |Θ◦⟩ can be related to the simple oscillator’s vacuum |0⟩ (i.e., a|0⟩ = 0) as |Θ◦⟩ = Ω(a†)|0⟩ (8) Find (up to a normalization factor) the operator function Ω(a†) relating two vacua. Hint: in working out Eqs.(7,8), employ Eqs.(1,2). Problem 3. Prove from the standard commutation relations ([ai; a † j ]∓ = ij , etc) that ⟨0|aiaja † ka † l |0⟩ = jkil ± ikjl (9) the sign depending on the statistics. Also calculate the vacuum expectation value ⟨0|ahaiaja † ka † l a† m |0⟩. Problem 4. In the formalism of second quantization the two-particle interaction term of the Hamiltonian for spinless fermions is given by ˆ V = 1 2 ∫ ∫ dxdy ˆ †(x) ˆ †(y)V(x; y) ˆ (y) ˆ (x) (10) For the short-ranged interaction V(x; y) = V(|x−y|) ≡ V(r) = e2 exp(−r)=r find ˆ V in the momentum representation. The field operators and the creation/annihilation operators in the momentum representation are related in the usual way, i.e., ˆ †(x) = ∫ dp (2)3 a†(p)e−ipx (11) Note that the limit  → 0 recovers the Coulomb (long-ranged) interaction V(r) = e2=r. What is the Fourier transform V(q) of the Coulomb interaction? 2 Problem 5. The matrix elements of a two-particle interaction from the previous problem can be written as ⟨k3k4|V|k1k2⟩ = (2)3(k1 + k2 − k3 − k4)V(q) (12) where q ≡ k3−k1 is the momentum transfer. Show that the diagonal part of the interaction operator ˆ V found on the previous problem in the k-representation, arises from momentum transfers q = 0 and q = k2−k1. Write down the two interaction terms and identify them as direct (q = 0) and exchange (q = k2 − k1) interactions. Draw the corresponding Feynman diagrams. Problem 6. Find the first correction to the temperature dependence of the chemical potential  of the degenerate ideal electron gas, assuming constant particle concentration ⟨N⟩=V . Express the result in terms of T and the zero-temperature chemical potential ◦. For the calculations the following formula (we set kB = 1) can be used: I ≡ ∫ ∞ 0 f(“)d” e(“−)=T + 1 = ∫  0 f(“)d” + 2 6 T2f′() + O(T4) (13) 3

## Course: PHYS 5426 — Quantum Statistical Physics Assignment #1 Instructor: Gennady Y. Chitov Date Assigned: January 15, 2014 Due Date: January 29, 2014 Problem 1. Prove [a; f(a†)] = @f(a†) @a† (1) [a†; f(a)] = −@f(a) @a (2) for arbitrary function f of operator which admits a series expansion. The Bose creation/ annihilation operators satisfy the standard commutation relations [a; a†] ≡ aa† − a†a = 1 (3) Hint: From Eqs.(1,2) one can figure out the corresponding commutation relations for the powers of creation/annihilation operators and then prove them by the method of mathematical induction. Note that for an arbitrary operator Aˆ: @A^n @A^ = nAˆn−1. Problem 2. In the presence of a constant external force acting on a one-dimensional oscillating particle its Hamiltonian becomes that of the so-called displaced oscillator, and the Schr¨odinger equation ˆH (q) = E (q) of the problem (cf. lecture notes) can be written in terms of dimensionless variables as ( − 1 2 d2 d2 + 1 2 2 − √ 2  ) () = ” () ; (4) where q = √ ~ m! and E = ~!”. a). Write the Schr¨odinger equation (4) in terms of the creation/annihilation operators of the harmonic oscillator ( = 0)  = √1 2 (a + a†) (5) d d = √1 2 (a − a†) (6) 1 Via a linear transformation to the new creation/annihilation operators ˜a†; ˜a preserving the bosonic commutation relations for ˜a†; ˜a map the problem (4) of the displaced oscillator onto that of a simple harmonic oscillator with new operators (˜a†; ˜a). b). Find the spectrum (eigenvalues) ” (E) of the displaced oscillator. c). Write the normalized eigenstates |n⟩ of the displaced Hamiltonian (4) via a† and the vacuum state |Θ◦⟩ of the new operators, i.e. ˜a|Θ◦⟩ = 0 (7) d). As follows from the completeness of the oscillator’s eigenstates, the vacuum state of the displaced oscillator |Θ◦⟩ can be related to the simple oscillator’s vacuum |0⟩ (i.e., a|0⟩ = 0) as |Θ◦⟩ = Ω(a†)|0⟩ (8) Find (up to a normalization factor) the operator function Ω(a†) relating two vacua. Hint: in working out Eqs.(7,8), employ Eqs.(1,2). Problem 3. Prove from the standard commutation relations ([ai; a † j ]∓ = ij , etc) that ⟨0|aiaja † ka † l |0⟩ = jkil ± ikjl (9) the sign depending on the statistics. Also calculate the vacuum expectation value ⟨0|ahaiaja † ka † l a† m |0⟩. Problem 4. In the formalism of second quantization the two-particle interaction term of the Hamiltonian for spinless fermions is given by ˆ V = 1 2 ∫ ∫ dxdy ˆ †(x) ˆ †(y)V(x; y) ˆ (y) ˆ (x) (10) For the short-ranged interaction V(x; y) = V(|x−y|) ≡ V(r) = e2 exp(−r)=r find ˆ V in the momentum representation. The field operators and the creation/annihilation operators in the momentum representation are related in the usual way, i.e., ˆ †(x) = ∫ dp (2)3 a†(p)e−ipx (11) Note that the limit  → 0 recovers the Coulomb (long-ranged) interaction V(r) = e2=r. What is the Fourier transform V(q) of the Coulomb interaction? 2 Problem 5. The matrix elements of a two-particle interaction from the previous problem can be written as ⟨k3k4|V|k1k2⟩ = (2)3(k1 + k2 − k3 − k4)V(q) (12) where q ≡ k3−k1 is the momentum transfer. Show that the diagonal part of the interaction operator ˆ V found on the previous problem in the k-representation, arises from momentum transfers q = 0 and q = k2−k1. Write down the two interaction terms and identify them as direct (q = 0) and exchange (q = k2 − k1) interactions. Draw the corresponding Feynman diagrams. Problem 6. Find the first correction to the temperature dependence of the chemical potential  of the degenerate ideal electron gas, assuming constant particle concentration ⟨N⟩=V . Express the result in terms of T and the zero-temperature chemical potential ◦. For the calculations the following formula (we set kB = 1) can be used: I ≡ ∫ ∞ 0 f(“)d” e(“−)=T + 1 = ∫  0 f(“)d” + 2 6 T2f′() + O(T4) (13) 3

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Question One: There are 4 legal reasons why an agreement would lack consideration. Your assignment is to list each of the four legal reasons. Provide a factual example for each of the four legal reasons. The factual example can be from the textbook, an actual case that you know about or you can make it up. a) An agreement would lack consideration if ___________    factual example: X and Y . . . . b) An agreement would lack consideration if ___________    factual example: X and Y . . . c) An agreement would lack consideration if ___________    factual example: X and Y . . . d) An agreement would lack consideration if ___________    factual example: X and Y . . . Question Two: Explain Promissory Estoppel. Be sure to include the elements required to prove promissory estoppel in your discussion. Question One: There are 4 legal reasons why an agreement would lack consideration. Your assignment is to list each of the four legal reasons. Provide a factual example for each of the four legal reasons. The factual example can be from the textbook, an actual case that you know about or you can make it up. a) An agreement would lack consideration if ___________    factual example: X and Y . . . . b) An agreement would lack consideration if ___________    factual example: X and Y . . . c) An agreement would lack consideration if ___________    factual example: X and Y . . . d) An agreement would lack consideration if ___________    factual example: X and Y . . .

## Question One: There are 4 legal reasons why an agreement would lack consideration. Your assignment is to list each of the four legal reasons. Provide a factual example for each of the four legal reasons. The factual example can be from the textbook, an actual case that you know about or you can make it up. a) An agreement would lack consideration if ___________    factual example: X and Y . . . . b) An agreement would lack consideration if ___________    factual example: X and Y . . . c) An agreement would lack consideration if ___________    factual example: X and Y . . . d) An agreement would lack consideration if ___________    factual example: X and Y . . . Question Two: Explain Promissory Estoppel. Be sure to include the elements required to prove promissory estoppel in your discussion. Question One: There are 4 legal reasons why an agreement would lack consideration. Your assignment is to list each of the four legal reasons. Provide a factual example for each of the four legal reasons. The factual example can be from the textbook, an actual case that you know about or you can make it up. a) An agreement would lack consideration if ___________    factual example: X and Y . . . . b) An agreement would lack consideration if ___________    factual example: X and Y . . . c) An agreement would lack consideration if ___________    factual example: X and Y . . . d) An agreement would lack consideration if ___________    factual example: X and Y . . .

Ans. All given agreements are not contracts. The agreement which … Read More...
Question One: There are 4 legal reasons why an agreement would lack assignment is to list each of the four legal reasons.  Provide a factual example for each of the four legal reasons. The factual example can be from the textbook, an actual case that you know about or you can make it up. a) An agreement would lack consideration if  ___________         factual example: X and Y . . . . b) An agreement would lack consideration if  ___________       factual example: X and Y . . . c) An agreement would lack consideration if ___________          factual example: X and Y . . . d) An agreement would lack consideration if ___________          factual example: X and Y . . .  Question Two: Explain Promissory Estoppel. Be sure to include the elements required to prove promissory estoppel in your discussion.

## Question One: There are 4 legal reasons why an agreement would lack assignment is to list each of the four legal reasons.  Provide a factual example for each of the four legal reasons. The factual example can be from the textbook, an actual case that you know about or you can make it up. a) An agreement would lack consideration if  ___________         factual example: X and Y . . . . b) An agreement would lack consideration if  ___________       factual example: X and Y . . . c) An agreement would lack consideration if ___________          factual example: X and Y . . . d) An agreement would lack consideration if ___________          factual example: X and Y . . .  Question Two: Explain Promissory Estoppel. Be sure to include the elements required to prove promissory estoppel in your discussion.

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Is there anything else you might say to prove you are right?

## Is there anything else you might say to prove you are right?

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3. Why is it impossible to prove that an imperative is categorical merely by appealing to examples or experience?

## 3. Why is it impossible to prove that an imperative is categorical merely by appealing to examples or experience?

Categorical Imperatives are known a priori–They are exposed by means … Read More...
1. Isolate GT1 in the equation ΔGT2 T2 − ΔGT1 T1 = ΔH ( 1 T2 − 1 T1 ). 2. True or False? ln (a + b) = ln a + ln b … prove your answer numerically. 3. What is the base-e logarithm of 250, ln 250? Prove that your result works numerically. 4. Solve for x in the following equation: e–ax = 1/T. 5. Simplify the right side of the function y = eAeC/eT and then use the ln to solve for T. 6. At what values of ϕ are the functions sin(ϕ) or cos(ϕ) equal to 0? At what values are they each equal to 1? 7. Linearize the following equation to find m and K from the slope and intercept: v = m[X]/(K + [X]). 8. Find the 1st and 2nd derivatives of y(x) = 3×4 – 2×2 + 15. 9. Identify the locations of minima and maxima for the function given in the problem above. 10. Find the derivative of the function y(x) = 3 ln (2×2). Ψ(x), [Ψ(x)]2, Ψ’(x), and Ψ’’(x). 12. Integrate 3/x from to 1 to 3. 13. What is the integral of 3×2 – 2x + 4 between -1 and 1? 14. Integrate the following function from 2 to 4: y = 3 cos x + x/2. (Don’t forget to check your calculator settings! Is it set for degrees or radians?) 15. Isolate like terms and integrate both sides of your resulting differential equation: dy/dx = – 4 x-1 y-3.

## 1. Isolate GT1 in the equation ΔGT2 T2 − ΔGT1 T1 = ΔH ( 1 T2 − 1 T1 ). 2. True or False? ln (a + b) = ln a + ln b … prove your answer numerically. 3. What is the base-e logarithm of 250, ln 250? Prove that your result works numerically. 4. Solve for x in the following equation: e–ax = 1/T. 5. Simplify the right side of the function y = eAeC/eT and then use the ln to solve for T. 6. At what values of ϕ are the functions sin(ϕ) or cos(ϕ) equal to 0? At what values are they each equal to 1? 7. Linearize the following equation to find m and K from the slope and intercept: v = m[X]/(K + [X]). 8. Find the 1st and 2nd derivatives of y(x) = 3×4 – 2×2 + 15. 9. Identify the locations of minima and maxima for the function given in the problem above. 10. Find the derivative of the function y(x) = 3 ln (2×2). Ψ(x), [Ψ(x)]2, Ψ’(x), and Ψ’’(x). 12. Integrate 3/x from to 1 to 3. 13. What is the integral of 3×2 – 2x + 4 between -1 and 1? 14. Integrate the following function from 2 to 4: y = 3 cos x + x/2. (Don’t forget to check your calculator settings! Is it set for degrees or radians?) 15. Isolate like terms and integrate both sides of your resulting differential equation: dy/dx = – 4 x-1 y-3.

No expert has answered this question yet. You can browse … Read More...