Homework Statement
In the real world trimolecular reactions are rare, although trimerizations are not. Consider
the following trimerization reaction in which three monomers of A combine to form the
trimer C,
A + A \Updownarrow B, where k1 and k-1 are the forward and reverse rate...
Homework Statement
find the general solution to x'=Ax; where A is a 3x3matrix: A=[0 1 1; 1 0 1; 1 1 0]
Homework Equations
det(A-lambda*I)=0
The Attempt at a Solution
i found the eigenvalues to be 2, -1, -1.
for lambda=2 i found the corresponding eigenvector to be a 3x1 martrix...
think there is a typo in the question it should be P(z)=P(0)exp(2k''z).
after squaring the phasor I get: P(z) = exp(2j(wt-k'z))exp(2k''z)
then i don't know what to do to get in right form.
Homework Statement
Show from general considerations that the attenuation of power in the rectangular waveguide (TE10 mode propagating in z-direction) is:
P(z)=P(0)exp(-2k''z)
where k'' is the imaginary part of the wavevector in the phasor exp(j(wt-kz))
Homework Equations
power is...
Homework Statement
Evaluate the integral with respect to x from 0 to infinity when the integrand is x^2/(1+x^6), using complex integration techniques.
Homework Equations
The Attempt at a Solution
I have no idea where to start. Please help!
Thank you both! Vela I had done it a longer way and then just realized your way would have been so much easier lol oh well. What does self adjoint mean again?
I got n+1/2 as my answer which i think is correct!?
Homework Statement
Evaluate <n|p^2|n>
where p is the momentum operator for the quantised harmonic oscillator.
Homework Equations
creation operator: a+|n>=sqrt(n+1)|n+1>
annihilation operator: a|n>=sqrt(n)|n-1>
The Attempt at a Solution
the operator p can be defined in terms of...
Homework Statement
A cow weighing 500kg gains 5kg/day and costs $1 a day to keep. the market price for the cattle is $15 per koliram, but is falling by 10cents per day. when should the cow be sold?
Homework Equations
The Attempt at a Solution
so the 500kg is the initial...
Homework Statement
one duck is situated in each of the four corners of a 2mx2m square pen. suddenly, each duck begins to chase its anticlockwise neighbour. all the ducks travel at the same speed.
(a) by defining the origin of an x-y coordinate system in the bottom left hand corner of the...
Homework Statement
After a volcanic eruption, the ash gradually falls to the ground euqally in all directions. the depth of the ash diminishes with the distance from the volcano such that at a distance r metres the depth is exp(-r^2). find the total volume of ash falling within 1 km of the...
Thank you Mark.
And turbo, it's urgent as I've tried to answer them and can't and don't want to just look them up online, I want to work them out myself and Physics Forums is good like that as it gives you hints but doesn't solve them for you. And it's for an exam in a few days and the lecturer...
URGENT - optimisation problem
Homework Statement
Find the point on the line y=4x+7 that is closest to the origin.
Homework Equations
The Attempt at a Solution
I am completely lost on where to start and what to minimise. It's for exam preparation!