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1. Bohr-Sommerfeld Rule

Homework Statement Imagine that force for is atom was ## F= - \frac{\beta}{r^4}##, rather than ##F=- \frac{ke^2}{r^2}##, and consider only circular orbits, it would remain true that ##L_n= n \hbar## a.) From Netwon's law find the relationship between ##T ##(Kinetic Energy) and ##V##, b.) Find...
2. Rigid Box Particle and Heisenberg Principle

Thank you for the information. Could you cite your sources? Also, can anyone else corroborate that the sources are right?
3. Rigid Box Particle and Heisenberg Principle

Thank you, Freunde. It agrees with Heisenberg equation. ## \Delta p \Delta x \geq \dfrac {\hbar}{2} = 5.272 \times 10^{-35} m^{2} \times \dfrac {kg}{s} ## ## \Delta p \Delta x= h/4 = 16.5 \times 10^{-35} \times m^{2} \times \dfrac{kg}{s} ##
4. Rigid Box Particle and Heisenberg Principle

k=π/a a≈(h/2)(1/Δp) ,a=2Δx 2Δx=(h/2)(1/Δp) Δp*Δx=(h/4) I still don't see it. Help, please.
5. Rigid Box Particle and Heisenberg Principle

Homework Statement For the ground state of a particle in a rigid box, we have seen that the momentum has a definite magni- tude (h/2π)k but is equally likely to be in either direction. This means that the uncertainty in p is Δp≈ (h/2π)k. The uncertainty in position is Δx≈ a/2. Verify that...
6. Mass & Energy

Homework Statement If an electron and proton (both initially at rest and far apart) come together to form a hydrogen atom, 13.6 eV of energy is released (mostly as light). By how much does the mass of an H atom differ from the sum of the electron and proton masses? What is the...

Why?
8. The Uncertainty Relation for Position and Momentum

Homework Statement The position of a 60-gram golf ball sitting on a tee is determined within +- 1μm. What is its minimum possi- ble energy? Moving at the speed corresponding to this kinetic energy, how far would the ball move in a year? Homework Equations ## K\geq\dfrac {\hbar ^{2}}...
9. Prove Speed Any Particle with Mass >0 is Always < c

Yes, I am looking for a robust proof. Thank you for your advice. I will consider it and re-work the solution.
10. Prove Speed Any Particle with Mass >0 is Always < c

I agree with darkexponent's question. Don't Physicist "just" discard answers that don't make physical sense? I will try your approach too, vela.
11. Prove Speed Any Particle with Mass >0 is Always < c

If E>pc, then pc/E <1. Then, the ratio of v/c <1 . For v/c <1, c>v or v<c. :> I am not sure what robust means, but I am ok with this one too.
12. Prove Speed Any Particle with Mass >0 is Always < c

I don't know the exact definition of a robust proof either, but I have heard it so many times in textbooks that I know there's a difference between a weak proof and a robust proof. I will try you approach, darkxponent. Can anyone tell me, if this proof is robust? Thank you all for your help. :)
13. Prove Speed Any Particle with Mass >0 is Always < c

How do I make this a robust proof?
14. Prove Speed Any Particle with Mass >0 is Always < c

I think I found the proof. ## E^{2}-E^{2}\dfrac {u^{2}} {c^{2}}=\left( mc^{2}\right) ^{2}## ## E^{2}\left(1-\dfrac{u^{2}}{c^{2}}\right)=m^{2}c^{4} ## ##\dfrac{E^{2}}{c^{6}}\left(c^{2}-u^{2}\right)=m^{2} ## ##\dfrac{E}{c^{3}}\left(\left(c-u\right)\left(c+u\right)\right)^{\dfrac{1}{2}} =m ##...
15. Prove Speed Any Particle with Mass >0 is Always < c

Ok, thanks. I will follow what vela and lbix suggested. Vela which second equation are you referring to?
16. Prove Speed Any Particle with Mass >0 is Always < c

I don't know how to proceed :/ dp= gamma (m*v_2 - m*v_1 ) dt= gamma(d t_0), by time dilation formula F=ma=dp/dt m du/dt = gamma( (m*v_2 - m*v_1 ) )/dt
17. Prove Speed Any Particle with Mass >0 is Always < c

I am required to use these equations:
18. Prove Speed Any Particle with Mass >0 is Always < c

Homework Statement Use: ##\beta =\dfrac {\overline {u}} {c}=\dfrac {\overline {p}c} {E}\&\&E^{2}=\left( pc^{2}\right) +\left( mc^{2}\right) ^{2}## Homework Equations The Attempt at a Solution Solving the second equation for E, I get: ##\left( \dfrac {E u} {c}\right) ^{2}+m^{2}c^{4}>0##...
19. Assume Classical Ideas of Space and Time (Ether)

Homework Statement My question is part C of problem 1.9: http://facultyfiles.deanza.edu/gems/lunaeduardo/4DHW.PDF Homework Equations Pythagorean Theorem? The Attempt at a Solution I have c vector of lightwave going upwards and v going rightwards forming a right angle with the other...

Thanks.
21. Special Relativity Moving Frames Question

Homework Statement I am sort of reviving this thread. https://www.physicsforums.com/showthread.php?t=182511 My question is the same. I understand and agree with what fisix responded a few years ago. Homework Equations cos( θ)= v_cart / v_bullet The Attempt at a Solution I can...