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  1. K

    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. K

    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?
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    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} ##
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    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. K

    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. K

    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...
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    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}}...
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    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.
  9. K

    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.
  10. K

    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.
  11. K

    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. :)
  12. K

    Prove Speed Any Particle with Mass >0 is Always < c

    How do I make this a robust proof?
  13. K

    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 ##...
  14. K

    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?
  15. K

    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
  16. K

    Prove Speed Any Particle with Mass >0 is Always < c

    I am required to use these equations:
  17. K

    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##...
  18. K

    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...
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    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...
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