a) Consider three operators A, B and Ĉ. Assume that they obey the following commutation relations [4,Ĉ]=iß [B,Ĉ]= iÀ A(AB)A(C) 2(À² +. Show that b) For a 1-dimensional system with general Hamiltonian H +V(x) 2m = d{xp) find dt Express your answer in terms of x, p and V . c) Using the relativistic relation between mass and energy E= mc² write down an uncertainty relation for mass and time. Assume that a free neutron has a life time of ~10° s. Estimate the uncertainty in the neutron's mass.

a) Consider three operators A, B and Ĉ. Assume that they obey the following commutation relations [4,Ĉ]=iß [B,Ĉ]= iÀ A(AB)A(C) 2(À² +. Show that b) For a 1-dimensional system with general Hamiltonian H +V(x) 2m = d{xp) find dt Express your answer in terms of x, p and V . c) Using the relativistic relation between mass and energy E= mc² write down an uncertainty relation for mass and time. Assume that a free neutron has a life time of ~10° s. Estimate the uncertainty in the neutron's mass.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Demonstrate the following relationships involving the determinate (a) Vector cross product (b)…

A: Since you have asked multiple questions, we will solve the questions (a) and (b) for you. If you…

Q: Describe how to find the Jacobian of x and y with respect to u and v for x = g(u, v) and y = h(u,…

Q: Set V = {(x, y) | x ER, YER}. Define addition of vectors by the rule (x, y) + (x, y) = (y + y',x+x')…

Q: [C] Is the system of vectors X1 = (2, 2, 1)", dependent? Ху — (1,3, 1)7, X3 = (1, 2, 2)" linearly

Q: Q1. Let u= (1, 1), addition and scalar multiplication on Vas; u+v=(₁+y₁-1, 2+2-1) and a.u = (ay,…

Q: 7. Given that a,b and are three vectors whereas is a scalar such that axř=b+ã and a = 2. By using…

A: Vector triple product is used

Q: Given the matrices: i) ii) 01 1 0 2 2 3 A 3 ^-(29) 8 - (-) -- »-( ) 01 B 0 = (²₂) D = 1 5 0 1 4 3…

A: a) Given that, A=010301-201B=210-143C=32D=23-15

Q: Suppose two vectors F and ü: r=3i+25-4k v = 2i - 1ĵ+3k where i, j, k are the unit vectors in the…

A: Since you have posted a question with multiple subparts, we will solve only the first three subparts…

Q: et L be the linear operator on R? defined by L(x1, x2) = (x1 + 2x2,3x1)* Find the matrix A…

Q: R² with TlCI)={, a) is 1?! n the Nillspoce oft! Given Ti R în the Nullspace ofT? b) Determine all…

A: A map T:R2→R2, with Tab=1111ab Then, we have to answer the…

Q: Q which af fre following always true? are a) suppose that the ċharaicteristić palynomial of matrix…

Q: 13. Given a matrix X and a vector y of appropriate dimensions, define f(w) = ||y – Xw||² %3D a. If X…

A: given a matrix X and a vector y of appropriate dimensions, define as fw=y-X w2 a) if X is N×k ,…

Q: (5). If A, B and A+B are each non-singular and the products are conformable, prove that (a). A(A +…

Q: Properties of Vector Addition and Scolar Multiplication. (a₁, 02, 03) and b=(b₁,b₂,bz) and ~₁B EIR.…

Q: 3.) a.) Solve the system: u = 3x+2y, v=x+4y For x and y in terms of u and v. Then find the value of…

Q: 2. Use abbreviated index notation to prove or disprove the following statements involving arbitrary…

A: Since there are multipart, so here find the solutions of first and second part.

Q: () (O (-- 1) The span in F of the vectors 2 is a plane. 2) If a, b is a basis of R2, there exists v€…

Q: DETERMINE WHETHER THE VECTORS GIVEN BELOW X² = ( ²₁ ) e ²₁ X ² (²) et + (88) tet SET OF SOLUTIONS OF…

Q: 2. Is it possible to determine a vector i so that vet is a solution to the system 2 X'(t) = (; )…

A: According to question, Given system, X '⇀t = 1243 X ⇀t

Q: Let I be the linear operator on R2 defined by L i). Find the matrix A representing I with respect to…

A: Calculation:

Q: If the vector K az+Lay+ Ma, shows the maximum increase rate and direction of the scalar V at point…

Q: 201 Give monsingural uragonal matrix. Call a diagonal matrix ever be 21) Show that ( (2) where x, y,…

A: A 2×2 matrix is diagonalisable if A has two different eigenvalues.

Q: Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis…

A: Given Data: H^=hω03i0-i30002 , B^=b07i1-i-i71+i1+i1-i6,D^ =002α02α 02α0-3α

Q: Stable molecules form when atoms arrange in a way to exert equal force on each other. One such…

Q: a) Given the following matrices a = -and c= nd 2. 3 and C = 2. i) AT C. i) 2(BC"). i) D if (2AB)" =…

Q: Let E2 be the new system {O;x',y'} obtained by rotating the (O;x,y} perpendicular coordinate system…

Q: function V(x,y,z) = x² + xy + yz and a vector A = x² + xy + yzź are given. a) Find VV(x, y, z). b)…

A: Given function v(x,y,z) is

Q: Write the system in vector matrix form: 21 4 e 21 3e 21 -e -4 e* 21 21 b) О x' 3e -4 e" X, 1 x 3e 4…

Q: 4. Draw the zeroclines (the functions of the vector space set equal to zero) for the following…

A: To draw the zeroclines for the given system of equations and find the equilibrium points, we need to…

Q: 16. As in Exercise 15, describe the solutions of the following system in parametric vector form, and…

Q: Q5) Answer true or false for the followings: i) in triple dot of vectors (A x B). C = (B x A). C,…

A: Given statements, (i) In triple dot of vectors (A×B)·C=(B×A)·C where the vectors A,B, and C are not…

Q: 3. Demonstrate the following relationships involving the determinate (a) Vector cross product (b)…

Q: C) Use the properties of deterrainates without expanding prove that a b C a+2x b+ 2y c+2y=0 X y Z

Q: 1) a) Let u= and v=, where c is an undetermined scalar. What value should c have if u is to be…

Question

a) Consider three operators A, B and C. Assume that they obey the following commutation
relations
[4‚Ĉ]= iß
[B,Ĉ] = iÀ
1
A(AB)A(C)2(À² + B*)
Show that
2
b) For a 1-dimensional system with general Hamiltonian H
+V(x)
2m
d(xp)
find
dt
Express your answer in terms of x, p and V .
c) Using the relativistic relation between mass and energy E = mc² write down an uncertainty
relation for mass and time.
Assume that a free neutron has a life time of ~10ʻ s. Estimate the uncertainty in the neutron’s
mass.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Ring$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

2i -1+iy -2 + i) are linearly independent over C ? -1+ 3i)
3) Please help with following multiple choice ASAP
Solve the vector spaces
Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis formed by the three kets {|e1>, |e2>, |e3>}. In the basis of these three vectors, taken in this order, the Hamiltonian H^ and the two operators B^ and D are defined by: H = ħwo 3 i 0 i 30 0 02 7 B÷bo -i i 1- i 1+ 6 | (0)) = 7 1+i 1 - i (e₁] (0)) (€₂ (0)) (€3) (0) 0 0 2α where wo and bo are constants. Also using this ordered basis, the initial state of the system is given by: = D 0 2α 2a 0 -3a Suppose that the initial state (0)> was left to evolve until t = 0. Q: After measuring operator Ô at t#0 and then B, what is the probability of finding the system in ground state?
Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis formed by the three kets {|e1>, |e2>, |e3>}. In the basis of these three vectors, taken in this order, the Hamiltonian H^ and the two operators B^ and D are defined by: H = ħwo 3 i 0 i 30 0 02 7 B÷bo -i i 1- i 1+ 6 | (0)) = 7 1+i 1 - i (e₁] (0)) (€₂ (0)) (€3) (0) 0 0 2α where wo and bo are constants. Also using this ordered basis, the initial state of the system is given by: = D 0 2a 2a 0 -3a Suppose that the initial state (0)> was left to evolve until t = 0. Q: After measuring operator Ô at t #0, the operator B was measured. What are the possible values of AB?
Solv
1)LetT(x, y, z) := (2x + y, x + y + z, y – 32) de R³ in R3be a linear operator. Considering the usual internal product in R3: a)Show that T is a self-adjoint operator but is not orthogonal. b}lf V = (2, –1,5)andw = (3,0, 1), · Make sure that (Tv, w) = (v,T'w). c) Display a base of eigenvectors and eigenvalues ofT and verify that it is an orthogonal base. From this base, find an orthonormal base.
Let c₁ (t) = esti + 3 sin(t)j + t7k and c₂(t) = e−³¹i + 2 cos(t)j – 8t¹k. (Enter your solution as a single vector using the vector form (*,*,*). Use symbolic notation and fractions where needed.) -[c₁ (t) + c₂ (t)] = dt
a) Find a spanning set for the plane in R' given by x- 3y+4z=0 b) Find the matrix of the projection operator onto this plane. c) Find the projection of the vector v= (1,1,1) onto the plane. d) Find the projection of the vector w= (1,-1,-1) onto the plane.
a) Consider a set of vectors R = {k, kx, kx, e**) where k is a scalar. i. Find the Wronskian, W(x) for the set. i. Find the range of k such that the set is linearly independent. b) Find the angle, e between vectors u = (2,5) and v = (1,2) with the Euclidean inner product (u, v) = 3u₂v₁ +2v₂u₁. State the orthogonality of the vectors. c) Express the vector v = (1,2,5) as a (1,2,3) and v3 = (2,-1,1). linear combination of v₁ = (1.1.1). V₂ =