# Search results

1. ### I Can this particular method solve these quadratic equations?

When substituting the solution for ##x## in the other equation, I get: $$y^2 \bigg(a'\cdot \frac{(-2h\pm s)^2}{4a^2}+2h'\cdot \frac{-2h\pm s}{2a}+b'\bigg)+c'=0$$ Where ##s=\sqrt{4h^2-4ab+\frac{4ac}{y^2}}##. Not sure how such an equation can be solved. Also, shouldn't a quartic equation have a...
2. ### I Can this particular method solve these quadratic equations?

Why does this solution for ##x## not have the form of a fraction? It's missing a factor of ##\frac{1}{2a}## as mentioned in my opening post, isn't that how the solution of a quadratic function is defined according to the abc-formula?
3. ### I Can this particular method solve these quadratic equations?

Thanks, but wouldn't this lead to another method to solve these equations? I was wondering whether the quoted method can actually be used to solve this.
4. ### I Can this particular method solve these quadratic equations?

You mean as in dividing ##S_1## and ##S_2## by either ##x^2## or ##y^2##? I have tried that but I'm not sure how to continue to get ##x## or ##y## on one side.
5. ### I Can this particular method solve these quadratic equations?

Given are two equations: $$S_1 = ax^2+2hxy+by^2 + c=0$$ $$S_2 = a'x^2+2h'xy+b'y^2 + c'=0$$ This source states that there are several methods to solve for ##x## and ##y##. One of them is the following quote:"Treat equation ##S_1## as a quadratic equation in ##x## and solve it for ##x## in terms...
6. ### I Correlation between Symmetry number & Total wavefunction

"proton or neutron" as in exchange of a proton pair "or" neutron pair? If yes, could you please elaborate how this quote is compatible with this: I am a bit confused.
7. ### I Correlation between Symmetry number & Total wavefunction

I understood that specific phrase "won't have to be" as in "not obliged to be" which made me think that it is also possible for such a model to be antisymmetric under exchange of a proton and neutron as well, just as in the exchange of a proton pair or neutron pair. But I assume you meant that...
8. ### I Correlation between Symmetry number & Total wavefunction

Does "won't have to" imply that it is still possible to stay antisymmetric? Because in that case, the classical symmetry number would still not have a clear link (to me) since it relies on the physical indenticality of particles.
9. ### I Correlation between Symmetry number & Total wavefunction

But whether the total wavefunction is symmetric/anti-symmetric depends on the spins of the nuclei, not on whether the nuclei are identical or not. It goes even further by the fact that the total wavefunction of e.g. dihydrogen can be symmetrical even if the two atoms have opposed spins. So it...
10. ### I Correlation between Symmetry number & Total wavefunction

Some rotational quantum states are not allowed for a rotating particle. At quantum level, these "forbidden" quantum states is based on the requirement of the total wavefunction being either symmetrical or anti-symmetrical, depending on whether the particle is a fermion or boson. The particle's...

24. ### Influence of vacuum in the Conservation of energy

@Cutter Ketch I have been thinking this through and I am curious about the validity of my deduced integral to calculate the work done on the small piston. The pressure force ##F_P## is the difference between the two pressures halves in the container times the surface of the small piston. These...
25. ### Influence of vacuum in the Conservation of energy

Thank you so much for your time and your clear explanations. This helped me
26. ### Influence of vacuum in the Conservation of energy

Ah, my bad. I was taking piston 2 's larger inertia to decelerate into account but I forgot that its larger area of force at pressure equilibrium would also compensate for that. One last question; if friction from the pistons on the walls are taken into account, would the distances swept out by...
27. ### Influence of vacuum in the Conservation of energy

Assuming both pistons would swipe the same volume to reach equlibrium, does this mean that piston 2 would move a distance that is a factor ##\frac{r^2_2}{r^2_1}## smaller than piston 1, even though they have the same initial acceleration? (again, no resisting forces added).
28. ### Influence of vacuum in the Conservation of energy

Ah ok. You said furthermore that it will show an oscillation when there's no friction. In the presence of friction, would this mean that the pistons would stop at positions where the pressure difference is zero?
29. ### Influence of vacuum in the Conservation of energy

Because you said in post #26 that the initial accelerations would be different in this scenario. Perhaps I have missed your point but I'm not sure how.
30. ### Influence of vacuum in the Conservation of energy

Could you please tell me what I'm donig wrong here? In the case of a pressure difference while holding the pistons and then releasing them to relax (without applying any additional forces) the pressure force on piston ##1## would be ##F_1 = (P_2 - P_1) \cdot \pi r^2_1 = m_1 \cdot a_1##. The...