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...