Recent content by Penny57

Could it be related to the fact that it has the lowest possible energy eigenvalue, so the system will naturally fall towards it? The ground state here, to my understanding, is a cosine-like wavefunction. I am assuming that means that, in order to connect to the exponential of the outside, there...

I know this wavefunction should behave as a symmetric cosine function (possibly as Cos( (k∗x)/(hbar) ?). I also know for a bound state, the wavefunction must decay exponentially outside the well. Additionally, r = (-β+ik)/(β−ik) . However, aside from that, I do not know how to get this question...

Thank you so much for the help! I've managed to work through it with the advice given. I forgot to account for the expression of the states - once I did, the problem became much easier. Thank you for the help! And that rule makes a lot more sense now. Thank you again!

For the first part of the problem, I managed to form this matrix; <1|O|1> <1|O|2> <2|O|1> <2|O|2> = 1 0 0 0 However, that was because I was following this image; I'm not entirely sure how this was obtained, and I'm not really sure what to do to continue forward with part e. I...

I see - thank you for the help! I understand what you mean the more I read it and apply it to the problem. I have just recently learned Taylor series, so I was a bit confused on its applications. I have a more solid grasp on the derivative part of your explanation, but I'll likely understand...

Taking the Taylor series expansion expansion about x = 0 led me to: -(2 * G * m * M) / a + 1/2 * (2 * G * m * M) / a^3 * x^2 (note - is there a way to show fractions in a more viewable format?) I also see why I should use G now, I had grown so accustomed to the formula the thought hadn't...

The relevant equations has been me working out the gravitational potential energy. I was told to take the derivative twice from here, but I do not understand why. It leads into a taylor series expansion, which seems excessive, but I was not informed on any other way to do it. Any advice would be...