Normalize the following function
(2−r/a0) e^−r/2a0 for 0 ≤ r ≤∞ , treating a0 as a constant
please show steps.
Normalize the following function (2−r/a0) e^−r/2a0 for 0 ≤ r ≤∞ , treating a0 as a...
Please solve the normalization, 7e, and the commutator
questions
6. Normalization Normalize the following functions: sin (1") between 0<x<L 200 for 0 <r <o, treating do as a constant 7. Eigenfunctions and Eigenvalues Determine which of the following are eigenfucntions of the operator 4 give the eigenfunction. Where appropriate (a) pikx (b) cos ka (c) k (d) kx (e) e-ax? 8. Commutator Evaluate the commutator (î, P2]
Please show all steps. Linear Algebra
Bonus: Let A E Mn(C) such that A0 for some positive integer m. Prove that An 0 Hint: What is the minimal polynomial for A?
. Consider the function v(r) r(r 1/2) (r-1) for r e (0, 1]. Determine the transformed function u(E) introduced in the previous question. Show that u(E)dE = 0. (Hint: you can do this without evaluating the function.) Determine the values of the midpoint rule,the simple trapezoidal rule (with two point s) and of the Gaussian rule with 2 quadrature points. What do you observe about the accuracy of these rules? 10pts
. Consider the function v(r) r(r 1/2) (r-1) for...
Normalize the following functions in the specified regions: (a) ψ (x) = x2 (from x = 0 to x = 2); (b) x ψ (x) = 1 (from x = 5 to x = 10); (c) ψ (r) = e−r / a (from r = 0 to ∞; a is a constant; volume element is 4πr2dr); (d) ψ (x) = cosax (from –π/2a to π/2a; a is a constant).
(1) The ground-state wave function for the electron in a hydrogen is given by ls 0 Where r is the radial coordinate of the electron and a0 is the Bohr radius (a) Show that the wave function as given is normalized (b) Find the probability of locating the electron between rF a0/2 and r2-3ao/2. Note that the following integral may be useful n! 0 dr =-e re /a roa r a Ta
Consider relation R = (A,B,C,D,E) for the following:
2. Is R in 2NF with the following functional dependencies? If not, normalize it. [5 points] A→BC -AD → E в с 3. Are the relations from the answer of question 2 in 3NF? If not normalize it. 5 points]
A. Normalize the wave function Ψ=Ae^(-ax^2) where A is the normalization constant and a is an integer. A= ? B. What is the expected value of the momentum? <p> = ?
(10 points) Normalize the wave function: Find the expectation values of (x), (r aj. Ģ) and (p2).
Real analysis
2. Consider the following three definitions: A function f : R-+R is lax-continuous at a E R provided for all e > 0 there is a 6 > 0 such that for all r E R, if x - al6 then |f(x)- f (a)e A function f : R - R is e-continuous at a E R provided for all e >0 there is a 6 > 0 such that for all r E R, if |a- a...
[10%) The radial part ofa wave function for an atom is given by (r)-Агет where A is the normalization constant and ag is a positive number. Calculate the expectation value of r for this state. A. 2a0 В. Зао C. 4ao D. 5ao (k