Evaluate the integral below between the limits t=0 to t (x=0) (x) Show that A+B → Products -d[A] dt dx dt K₂ = K₂ [A][B] = = K₂(a - x)(b - x) 1 = b(a - x) -In t(a - b) a (b − x)
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![Evaluate the integral below between the limits t=0 to t
(x=0) (x)
Show that
A+B
-d[A]
dt
dx
dt
=
K₂ =
Products
=
= K₂ [A][B]
K₂ (a − x)(b − x)
1
t(a - b)
- In
b(a - x)
a(b - x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4bca224-9729-4164-9eec-3aa9dc328bac%2F4fe657ff-c054-487a-a5db-7065b20e509a%2Fhwqgbl4_processed.png&w=3840&q=75)
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- Determine whether the function f:(-1,00) → R defined by f(x) = 3 x+1-e 3 + x is concave or convex. c (a) f: (-1,00)→ R defined by f(x) = 3√√x+1-e-4x + x.Normalize the wave function e-ax in the range 0≤x≤ ∞, with a > 0.Consider the simple functions below, f(x) = x? (1) f(x) = x³ (2) f(x) = x* + 2x3 (3) f(x) = sin(x) (4) f(x) = cos(x) (5) f(x) = e* (6) f(x) = sin(x) + cos(x) (7) f(x) = cos (x) + sin?(x) (8) f(x) = cos(x) +1 (9) f(x) = sin(x) + x (10) (a) Of the ten which function(s) are odd. Indicate them by their equation number and draw a box around your answer. (b) Of the ten which function(s) are neither even nor odd. Indicate them by their equation number and draw a box around your answer.
- Identify the systems for which it is essential to include a factor of 1/N! on going from Q to q : (i) a sample of carbon dioxide gas, (ii) a sample of graphite, (iii) a sample of diamond, (iv) ice.Which of the following statements describe principles or rules you should consider when writing an electron configuration? Select all that apply. Multiple answers: Multiple answers are accepted for this question Select one or more answers and submit. For keyboard navigation... SHOW MORE v a no two electrons can have the same spin in the same orbital b electrons occupy orbitals from higher to lower energy levels electrons should be divided among different orbitals within the same subshell to avoid pairing if possible d electrons occupy orbitals from lower to higher energy levels e paired electrons must have the same spin One more question about sulfur! Which of the following pictures represent orbitals in a sulfur atom in its ground state? Select all that apply. A. В. C. D. Е. B.Evaluate the following commutators d (a) | x, dx d (b) | х, dy d (c) dx d + x dx -
- A two-level system is in a quantum state = α₁₁ + a22, which can be represented by the vector a = {a1, a2}. We are looking for the conditions under which is eigenstate of the operator c., defined below. 1) In the expression c.ỗ, c is a vector with components {Cr, Cy, Cz} ( C; are real numbers) and ỗ is a vector with components {σx, σy,σz} (σ¿ are 2 × 2 matrices). This means that the operator c. can also be represented by a 2 × 2 matrix. Write the matrix of the operator c. knowing that 0 0x = = (₁ }) = ( 5 ) . Oy σz= 0 (6-99) 1 0 1 0 2) In matrix form, the eigenvalue equation is AX AX, where A is the matrix of the operator of interest, X the column matrix representing the eigenvector and the corresponding eigenvalue. Write the eigenvalue equa- tion that needs to be verified for the quantum state to be an eigenvector of the operator c.. = 3) Note that AX = XX ⇒ (A - I)X 0, where I is the identity matrix. (AAI)X=0 is true if and only if det(A - I) = 0. Solve this equation for the operator…P7F.9 In this problem you will establish the commutation relations, given in eqn 7E. 14, between the operators for the x-, y-, and z-components of angular momentum, which are defined in eqn 7F.13. In order to manipulate the operators correctly it is helpful to imagine that they are acting on some arbitrary function f: it does not matter what fis, and at the end of the proof it is simply removed. Consider [,,1,] = ,-11. Consider the effect of the first term on some arbitrary function fand evaluate A D -x dx se The next step is to multiply out the parentheses, and in doing so care needs to be taken over the order of operations. (b) Repeat the procedure for the other term in the commutator, 1,1, f. (c) Combine the results from (a) and (b) so as to evaluate l f-11f;you should find that many of the terms cancel. Confirm that the final expression you have is indeed iħl_f, where l̟ is given in eqn 7F.13. (d) The definitions in eqn 7E.13 are related to one another by4. A one-particle, one-dimensional system has the state function. 1 e y = sin(at) (2) 4: 32 1 + cos (at) (2) 4 x xe Where a is a constant and c-2.000 Å. If the particle's position is measured at t=0, estimate the probability that the result will between 2.000 Å and 2.0001 Å. (This range can be thought of as infinitesimal process)
- Define the term lambda max (λmax)(a) Consider the translational motion of a particle in a one-dimensional box of mass m, that is free to move between x = 0 and x = L: (i) State the boundary conditions that must be satisfied. (1) (ii) Draw rough sketches of three different boxes to illustrate the relationship between the energy separation and the increasing or changing length of the box. (3)Consider a particle in a one dimensional box of length ‘a' with the following potential V(x) = ∞ x a is (a) V₁ 0≤x≤a/2 a/2≤x≤ a Starting with the standard particle in a box hamiltonian as the zeroth order Hamiltonian and the potential of V, from 'a/2' to 'a' as a perturbation, the first-order energy correction to the ground state (b) V₁/4 (c) -V₁ (d) V₁/2