How do i go about proving that none of the principal moments of inertia can exceed the sum of the other two?
Someone suggested the triangle inequality, but i don't understand how to use it.
yeah, dots are derivatives with respect to time..but which function do i integrate to get velocity? i mean i can integrate the second one (acceleration ) to get velocity, but even then, it's in terms of x rather than time..i want velocity versus time so how do i go about getting that
So my problem is: a mass M that is fired at 45 degrees with KE E_0, at the top of the trajectory, projectile explodes with additional energy E_0 into two parts, the first fragment travels straight down , what is the velocity of the the first and the velocity and direction of the second part...
SO i basically need to know what the graph of velocity vs time is..and I'm supposed ot do this numerically using maple...though if anyone has some basic intuition about what the graph should look like, even that would be nice.
Anyways, I'm unsure of how to graph it
Basically i have x_dot^2...
so you basically a friend showed me what they did but i still don't really understand how they got Cn for this equation without integrating. I think they set the constants equal to what was already in Psi(x,0), but it was really hard to place all the factors they got
Second question..i've noticed in the book it says i can write Psi(x,0) as a linear combination of stationary states. So I'm trying to tell what linear combination this function is. However, i was wondering if anyone had the 2nd stationary state handy. I calculated it but am unsure if it is...
I'm still really confused on how to go about calculating this for non eigenstates. I'm trying to do the problem below, and am wondering how to go about it.
\Psi (x,0) = A (1-2 \sqrt {\frac{m \omega}{\hbar}} x)^2 e^ {-\frac{m \omega x^2}{2 \hbar}}
So I can't calculate the expectation...
I've read the chapter but it hasn't helped. Eigenstates are states with a definite amount of energy independent on time? and then any other state is a linear combination of the eigenstates, with some Cn acting as a weighting factor...is there a limitation on what the Cn's can be? otherwise...
question: how do you prove that odd N numbered solutions to the harmonic oscillator are odd? It's not necessary to solve this problem, but I'm trying to remember what my teacher said about it. I assume that you can prove that A_+ \psi_0 is odd, while A_+^2 \psi_0 is even.
lol you i didn't notice it either..i just looked for other things..slashes are all the same to me:)
and thanks for the help..i'll figure it out bit by bit
So i was working on a homework problem to calculate energy, and i can calculate it directly. But i was thinking it should be easier to use the number operator on the wave function and find out what it's energy should be. The function involved is the initial wave state of a quantum harmonic...
So i was working on a homework problem to calculate energy, and i can calculate it directly. But i was thinking it should be easier to use the number operator on the wave function and find out what it's energy should be. The function involved is the initial wave state of a quantum harmonic...