- #1
yxgao
- 122
- 0
Why does the half of a harmonic oscillator potential allow only odd values of n?
Thx
Thx
Why Does a Half Harmonic Oscillator Only Allow Odd Quantum Numbers?
- Thread starter yxgao
- Start date
AI Thread Summary
A half harmonic oscillator potential only allows odd quantum numbers due to the boundary condition that the wave function must be zero at the origin, where the potential is infinite. This restriction leads to the acceptance of only odd solutions from the full harmonic oscillator's wave functions. The discussion humorously notes the timing of the question, suggesting a break from quantum mechanics during the holiday season. The emphasis is on understanding the implications of the potential's shape on the allowed quantum states. Thus, the odd quantum numbers arise directly from the requirement that the wave function vanishes at the boundary.
- #2
dextercioby
Science Advisor
- 13,394
- 4,062
yxgao said:
1.What do you mean by "half of a harmonic oscillator"??You should have written the text of the problem so anyone could figure it out...
2.Today it's Christmas Day.Leave QM for tomorrow at least...
Are u going to solve QM problems on the New Year's Eve too?? Daniel.
NO QUANTUM MECHANICS ALLOWED ON CHRISTMAS!
- #3
Triss
- 80
- 0
If you mean half of a harmonic oscillator potential where V(0)=\infty, then looking at the wave functions for the full harmonic oscillator you can only admit those solutions where \psi(0)=0. That will give you the odd solutions.
Here we know that if block B is going to move up or just be at the verge of moving up
##Mg \sin \theta ## will act downwards and maximum static friction will act downwards ## \mu Mg \cos \theta ##
Now what im confused by is how will we know " how quickly" block B reaches its maximum static friction value without any numbers, the suggested solution says that when block A is at its maximum extension, then block B will start to move up but with a certain set of values couldn't block A reach...
TL;DR Summary: Find Electric field due to charges between 2 parallel infinite planes using Gauss law at any point
Here's the diagram. We have a uniform p (rho) density of charges between 2 infinite planes in the cartesian coordinates system. I used a cube of thickness a that spans from z=-a/2 to z=a/2 as a Gaussian surface, each side of the cube has area A.
I know that the field depends only on z since there is translational invariance in x and y directions because the planes are...
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system
$$M(t) = M_{C} + m(t)$$
$$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$
$$P_i = Mv + u \, dm$$
$$P_f = (M + dm)(v + dv)$$
$$\Delta P = M \, dv + (v - u) \, dm$$
$$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$
$$F = u \frac{dm}{dt} = \rho A u^2$$
from conservation of momentum , the cannon recoils with the same force which it applies.
$$\quad \frac{dm}{dt}...
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