What would be the energy eigenvalues of this particle?

AI Thread Summary
The discussion centers on determining the energy eigenvalues of a particle confined in a 3D box with dimensions L, 2L, and 2L. The initial assumption presented was that the energy eigenvalues could be expressed as hcross*w*A. However, a participant corrected this by providing the accurate formula for the energy eigenvalues, which is (h^2/8m)(n_1^2/L^2 + n_2^2/4L^2 + n_3^2/4L^2), where n_1, n_2, and n_3 are quantum numbers. The original poster expressed gratitude for the clarification. The thread effectively highlights the importance of precise calculations in quantum mechanics.
FUNKER
Messages
120
Reaction score
0
howdy all,
i need some answers if possible
suppose i have a particle mass m, confinded in a 3d box sides L,2L,2L
what would be the energy eigenvalues of this particle
i presumed it to be:

hcross*w*A
where hcross is h/2*pi
w is omega
and A is the 'amplitude' of the wavefunction.
can someone confirm this or tell what it may actually be
thanks
peace
 
Physics news on Phys.org
Your answer is not correct, the correct answer should be.
\frac{h^2}{8m}(\frac{n_1^2}{L^2}+\frac{n_2^2}{4L^2}+\frac{n_3^2}{4L^2}),
n_1=1,2..., n_2, n_3 are the same.
 
Last edited:
hey thanks heaps for your help brother
peace
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

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}...
View full post »

Similar threads

Speed of a hanging rope sliding on a nail (using energy conservation)
Replies
6
Views
2K
Partition function of a particle with two harmonic oscillators
Replies
2
Views
2K
Ground state energy eigenvalue of particle in 1D potential
Replies
6
Views
2K
How to calculate quality factor for RLC circuit?
Replies
6
Views
1K
I Solving a Particle on the Surface of a Sphere: Obtaining Eigenvalues
Replies
4
Views
2K
I It seems that the eigenvalue problem rules out the possibility of E=0?
Replies
5
Views
1K
How do you calculate Electric Potential Energy in a Square?
Replies
2
Views
4K
Energy eigenstates of a particle in a one dimensional box.
Replies
12
Views
3K
[PoM] Average rotational energy
Replies
1
Views
1K
Misunderstanding of Gravitational Potential Energy
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top