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- Please offer an easy and concise explanation for part a only! I understand part b alreadyConsider 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.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 by
- Define the term lambda max (λmax)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.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…
- Two nitro (NO,) groups are chemically bonded to a patch of surface. They can't move to another location on the surface, but they can rotate (see sketch at right). It turns out that the amount of rotational kinetic energy each NO, group can have is required to be a multiple of s, where e= 1.0 x 10* J. In other words, each NO, group could have e of rotational kinetic energy, or 26, or 3ɛ, and so forth – but it cannot have just any old amount of rotational kinetic energy. Two rotating NO, groups Suppose the total rotational kinetic energy in this system is initially known to be 198. Then, some heat is added to the system, and the total rotational kinetic energy rises to 27e. Calculate the change in entropy. bonded to a surface. Round your answer to 3 significant digits, and be sure it has the correct unit symbol.Snitial Sinal В Sfinal A Sanal Sfinal 13V3 Based on the image, which system has a AS of zero?What is the eigen value when the eigen function e* is operated on the operator d" | dx" ? (А) а " (B) а" (C) a-*n (D) na