- #1
Claire84
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Hey there.
As part of our quantum assignment we;ve to also look at a simple classical oscillator (it's part b to a question about the one dimensional harmonic oscillator). Problem is, I can hardly remember a thing that isn't to do wih quantum! So any help here would be appreciated. We've to find an expession for the velocioty of the particle as a function of positon, and I think I'm going okay with it, it's just the limits that I don't know about (maximum displacements are a and -a).
I've got it down to v(dv/dx)= (-w^2)x which gives me vdv=(-w^2)xdx, but I don't know which way to integrate between the limits. Is the amplitude at the bottom or the top? The example of it I looked at online as x as the upper limit and the amplitude as the bottom one, but I don't get that...
Secondly, we've to (as a result fo the first bit), show that the probability of locating the particle in an interval dx between the maximum displacements a and -a is given by the ewt P(x)dx=dx/(pi(a^2 - x^2)^(1/2)). I'd like to take a stab at it but I don't know how to work out the probability for it - is it related to the probability that we use in quantum mechanics? Sorry, I sound so dumb here but I've no idea how to work out the probability. I've checked the net but to no avail. Please help (it would be much appreciated!)!
Claire
As part of our quantum assignment we;ve to also look at a simple classical oscillator (it's part b to a question about the one dimensional harmonic oscillator). Problem is, I can hardly remember a thing that isn't to do wih quantum! So any help here would be appreciated. We've to find an expession for the velocioty of the particle as a function of positon, and I think I'm going okay with it, it's just the limits that I don't know about (maximum displacements are a and -a).
I've got it down to v(dv/dx)= (-w^2)x which gives me vdv=(-w^2)xdx, but I don't know which way to integrate between the limits. Is the amplitude at the bottom or the top? The example of it I looked at online as x as the upper limit and the amplitude as the bottom one, but I don't get that...
Secondly, we've to (as a result fo the first bit), show that the probability of locating the particle in an interval dx between the maximum displacements a and -a is given by the ewt P(x)dx=dx/(pi(a^2 - x^2)^(1/2)). I'd like to take a stab at it but I don't know how to work out the probability for it - is it related to the probability that we use in quantum mechanics? Sorry, I sound so dumb here but I've no idea how to work out the probability. I've checked the net but to no avail. Please help (it would be much appreciated!)!
Claire