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2) In each case below show (in the space provided directly) that F(y) is an eigen-...
both pls 1) Which of the following operator(s) is/are Hermitian? a) id/dy? b) d/dy2 c) id/dy...
both pls
1) Which of the following operator(s) is/are Hermitian? a) id/dy? b) d/dy2 c) id/dy You may assume that the functions on which these operators operate are appropriately well behaved at infinity. (Hint #1: .. P dy = f. y pudy where the integral hudu = Uv - Sudv. Hint #2: Use y = e) 2) In each case below show (in the space provided directly) that F(y) is an eigen- function of the operator A and find the...
(( 8)) In each case show that F(x) is an eigen-function of the operator and find...
(( 8)) In each case show that F(x) is an eigen-function of the operator and find the eigen-value F(x) Eigen-value i) d/dx? cos ax ii) d/dt elat iii) d/dx2 + 2d/dx + 3 ex iv) d/dy xey v) V2 - d/dx2 + d´/dy2 + d´/dz2 cos ax cos by cos cz
18) Show that the following wave function y (3cos20 -1) is an eigen-function of the operator...
18) Show that the following wave function y (3cos20 -1) is an eigen-function of the operator P-h2 (d2/d02 + cot 0 d/de ). What is the eigen-value? (Hints: Use the following eigen-value equation, Py py and obtain an expression for p; cote-cose/sin0).
please show all work thank you 2. (4 points each) In the space provided, take the...
please show all work thank
you
2. (4 points each) In the space provided, take the derivative of each of the following functions. Make sure to use the appropriate notation for the derivative of the given function. (a) y = sin(x2 – 7) (b) y = (cos x)(tan x) (c) g(x) = (d) G(x) = sin? (720) 3х (e) y = x2 (f) F(p) = (1 – 4p2)3 (g) y = [arctan(t)][In(5t)] – 4 (h) f(x) = V5x3 – 7x...
Below are eight functions. Find the first derivative of each. Space is provided. Use good dark ink...
Below are eight functions. Find the first derivative of each. Space is provided. Use good dark ink if you are returning this by a scanned version. All of the derivatives can be found by using combinations of the constant rule, power function rule and sum-difference rule. Do not use the product rule. It is not needed. The degree of difficulty (more or less) increases from (a-h). Be sure to show intermediate work. Check the scoring rubric to see how the points are awarded. For example, the first...
Fx 0. Show that =-- dx Fy dy 8. Suppose y is a function of z, F(x, y) = 0, and F,メO. Show that d...
Fx 0. Show that =-- dx Fy dy 8. Suppose y is a function of z, F(x, y) = 0, and F,メO. Show that dr--Fr 9. Fid the critical points of f(z, y) if any exist, for (a, y) = ex sin y 10. Calculate the iterated integral: ysin(zy)d dy
Fx 0. Show that =-- dx Fy dy 8. Suppose y is a function of z, F(x, y) = 0, and F,メO. Show that dr--Fr 9. Fid the critical points...
Answer the questions in the space provided below. 1. The definition of a function f: X...
Answer the questions in the space provided below. 1. The definition of a function f: X + Y is as a certain subset of the product X x Y. Let f: N + N be the function defined by the equation f(n) = n2. For each pair (x, y) listed below, determine whether or not (x,y) ef. a) (2,4) b) (5, 23) c) (1,1) d) (-3,9) 2. For each function defined below, state whether it is injective (one-to-one) and whether...
#4 4) Show that: a) The classical kinetic energy = (1/2). muy is equal to py/2m. Here py is the linear momentum in t...
#4
4) Show that: a) The classical kinetic energy = (1/2). muy is equal to py/2m. Here py is the linear momentum in the y-direction. b) Show that the Classical kinetic energy operator (1/2).muy is equal to the quantum mechanical kinetic energy operator = -1°/8x'm d/dy?. (Hints: Use the definition for momentum operator of the particle py=- (ih/2x) d/dy in quantum mechanics). c) Determine if A and B commute: if A = d/dy?, B = y, and f(y) = 30y...
7 marks (4 marks) (3 marks) (a) Is the operator P(v) y'+2ty linear? (Show workings) (b) Find the ...
please answer question 1) to 3) fully step by step
7 marks (4 marks) (3 marks) (a) Is the operator P(v) y'+2ty linear? (Show workings) (b) Find the null space of the operator in (a) above. Question 2 5 marks Let P be a linear operator. Suppose that y is a particular solution to the equation Ply) = b. Prove that any solution to this equation can be written as y = Yo + yi for yo au clement of...
. Let F(a,y)-(3e +secztan,e -90 (a) Show that F is a conservative. (b) Find a function f (potenti...
. Let F(a,y)-(3e +secztan,e -90 (a) Show that F is a conservative. (b) Find a function f (potential function) show that F (c) Use above result to evaluate Jc F. V. dr, where C is a smooth curve that begin at the point (2, 1 ) and ends at (0,3). (cos t, sin t) fromtto t particle that moves along the curve. (Write the value of work done without evaluating (d) Find the work done by the force field F(r,...
both pls
1) Which of the following operator(s) is/are Hermitian? a) id/dy? b) d/dy2 c) id/dy You may assume that the functions on which these operators operate are appropriately well behaved at infinity. (Hint #1: .. P dy = f. y pudy where the integral hudu = Uv - Sudv. Hint #2: Use y = e) 2) In each case below show (in the space provided directly) that F(y) is an eigen- function of the operator A and find the...
(( 8)) In each case show that F(x) is an eigen-function of the operator and find the eigen-value F(x) Eigen-value i) d/dx? cos ax ii) d/dt elat iii) d/dx2 + 2d/dx + 3 ex iv) d/dy xey v) V2 - d/dx2 + d´/dy2 + d´/dz2 cos ax cos by cos cz
18) Show that the following wave function y (3cos20 -1) is an eigen-function of the operator P-h2 (d2/d02 + cot 0 d/de ). What is the eigen-value? (Hints: Use the following eigen-value equation, Py py and obtain an expression for p; cote-cose/sin0).
please show all work thank
you
2. (4 points each) In the space provided, take the derivative of each of the following functions. Make sure to use the appropriate notation for the derivative of the given function. (a) y = sin(x2 – 7) (b) y = (cos x)(tan x) (c) g(x) = (d) G(x) = sin? (720) 3х (e) y = x2 (f) F(p) = (1 – 4p2)3 (g) y = [arctan(t)][In(5t)] – 4 (h) f(x) = V5x3 – 7x...
Fx 0. Show that =-- dx Fy dy 8. Suppose y is a function of z, F(x, y) = 0, and F,メO. Show that dr--Fr 9. Fid the critical points of f(z, y) if any exist, for (a, y) = ex sin y 10. Calculate the iterated integral: ysin(zy)d dy
Fx 0. Show that =-- dx Fy dy 8. Suppose y is a function of z, F(x, y) = 0, and F,メO. Show that dr--Fr 9. Fid the critical points...
Answer the questions in the space provided below. 1. The definition of a function f: X + Y is as a certain subset of the product X x Y. Let f: N + N be the function defined by the equation f(n) = n2. For each pair (x, y) listed below, determine whether or not (x,y) ef. a) (2,4) b) (5, 23) c) (1,1) d) (-3,9) 2. For each function defined below, state whether it is injective (one-to-one) and whether...
#4
4) Show that: a) The classical kinetic energy = (1/2). muy is equal to py/2m. Here py is the linear momentum in the y-direction. b) Show that the Classical kinetic energy operator (1/2).muy is equal to the quantum mechanical kinetic energy operator = -1°/8x'm d/dy?. (Hints: Use the definition for momentum operator of the particle py=- (ih/2x) d/dy in quantum mechanics). c) Determine if A and B commute: if A = d/dy?, B = y, and f(y) = 30y...
please answer question 1) to 3) fully step by step
7 marks (4 marks) (3 marks) (a) Is the operator P(v) y'+2ty linear? (Show workings) (b) Find the null space of the operator in (a) above. Question 2 5 marks Let P be a linear operator. Suppose that y is a particular solution to the equation Ply) = b. Prove that any solution to this equation can be written as y = Yo + yi for yo au clement of...
. Let F(a,y)-(3e +secztan,e -90 (a) Show that F is a conservative. (b) Find a function f (potential function) show that F (c) Use above result to evaluate Jc F. V. dr, where C is a smooth curve that begin at the point (2, 1 ) and ends at (0,3). (cos t, sin t) fromtto t particle that moves along the curve. (Write the value of work done without evaluating (d) Find the work done by the force field F(r,...
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