Ok thanks for that, the equation issue was bugging me for ages haha. Also thanks for the help vela and grzz I think I understand how operators work now.
So going from my original approach if i continue from:
-i\hbar\frac{\delta\psi}{\psi}=andx
then integrate through I get:
-i\hbarln\psi+constant=anx+constant
divide through by -i\hbar and move the constant from the LHS to the RHS giving:
ln\psi=\frac{anx}{-i\hbar}+constant
convert into...
So are you saying that -iℏ(δ/deltax) shouldnt change to ℏeianx since its acting on the eigenfunction of the same operator? Sorry if this is wrong just trying to understand what you said.
Homework Statement
A free particle (de Broglie wave) may be represented by the wave-function
\psi(x)=Aeikx
Show that this is an eigenstate of the momentum operator \hat{p}=-\hbar\frac{\delta}{\deltax}
Homework Equations
\hat{p}un(x)=anun(x)
an is the eigenvalue
un(x) is the corresponding...
Homework Statement
Designers of electrical circuits often take the maximum amplitude of the radiated electric field (at a large distance r) produced by an alternating current I0 flowing in a loop of area A cm2 to be given by
E=\frac{2.6AI0f2}{r}\muVm-1
where f is the frequency in MHz...
Homework Statement
A tunnel is bored through the centre of the Earth from Liverpool to New Zealand and a travel pod is dropped into it. The gravitational force on the pod is proportional to its distance from the centre of the Earth and so it undergoes simple harmonic motion described by...
I think I will stick with exp then, it doesn't really indicate what type of wave eqution to use so I think any type would suffice as long as it contained the given properties, especially considering the question before it uses sin and the question after uses exp.
It doesn't say you can't. Didn't think about using sine, been so used to the format of exp wave equations that involve finding out or using the phase velocity that it slipped my mind. Thankyou.
I understand this but how can I reflect part e) in the wave equation without tampering with the amplitude since as far as I can remember the "A" in the equation is just amplitude, no need to do any equation seperately for it and with x=0 and t=0, it cant be any other number. Any extra hints...
Homework Statement
Write down an equation to describre a wave \psi(x,t) with all of the following properties
a) It is travelling in the negative x direction
b) It has a phase velocity of 2000ms-1
c) It has a frequency of 100kHz
d)It has an amplitude of 3 units
e) \psi(0,0)= 2 units...
Thanks for explaining clearly which equation is for which. I just now went through converting the energy to the rydberg constant (per m) and it turns out it was alot easier than I initially thought. Also im very grateful for the code you've displayed regarding fractions on here. It turns out I...
Homework Statement
The ionisation energy of a single hydrogen atom is 13.6 eV. The application of Bohr quantisation to the hydrogen atom results in the stationary states having discrete energies given in terms of a positive integer n according to
E=-RB/n2
where RB is the Rydberg...
(b) The frequency of sound waves received by a detector when both source and detector move
relative to the air is:
f=f0[u(+ or -)vd/u(+ or -)vs] . Two trains are approaching each other at a level
crossing and blow their whistles at a frequency of 500 Hz. Train 1 is travelling at 20% of the...
Homework Statement
Question 1
(a) The displacement of a transverse wave on a string is described by:
y(x, t) = 0.01 sin(4x + 200t + \pi), where all quantities are expressed in SI units.
i) Determine values (with appropriate units) for the period, wavelength, and phase
velocity of the wave...
Thanks for that. I knew I had a problem with over complicating the working out and not thinking about the basics but I didn't know I was this bad. I'll have to remind myself for future reference to start thinking at the most basic level and work my way up instead of just assuming its harder than...
Honestly It was first instinct barely any thought put into it. The only thing I can think of is a distance of 4mm as its the total of both radius of each ball. But that still doesnt make sense considering its where contact was made and the center of each ball is clearly not where contact was...
Thanks for the help, the amount of stuff I got wrong here is woefully bad haha. I recall the equation \DeltaU=q\DeltaV now except I used to know it as \DeltaW=q\DeltaV from A levels and thats what probably threw me off since Im now used to doing potential energy as \DeltaU not \DeltaW. Anyways...
Homework Statement
The potential caused by an array of charges in a region of space can be described by the equation V(x,y,z)=2x+xy+y2-xz2 volts, where all distances are measured in metres. If a charge of 2 mC is moved from the position r1=(1,2,0)m to r2=(3,1,0), calculate the resulting change...
Homework Statement
During a collision between two initially uncharged polystyrene balls of radius 2 mm, some electrons are transferred from one of the balls to the other. In what direction does the resulting electrostatic force between the balls act?
The magnitude of the force between the...
Thanks for the help. I'll make sure next time to include my working out, I know it needs to be done in the exam but for some reason I decided to post just the answer here. Always good to be notified though as a reminder. :smile:
Homework Statement
Assuming that the orbits of the Earth, and of Jupiter, around the Sun are circular and given that Jupiter orbits with a radius 5.2 times that of the Earth, calculate the orbital period of Jupiter around the Sun.
Homework Equations
T2=(4(pi)2/(G*M))*r3
The Attempt...