Recent content by tut_einstein

Thanks Shyan and TheDuck, I understand that infinitesimal distances away from a given point isn't considered non-local, which is why the kinetic term isn't non-local. But if we expand the square root of the gradient, why can't we do the taylor expansion assuming that the displacement from a...

Hi, I have a quick question about making quantum mechanics relativistic by simply replacing the hamiltonian by a relativistic hamiltonian. If we write the hamiltonian operator as: H = \sqrt{P2c2 + m2c4}, Schrödinger's equation in position basis becomes: i\hbar\dot{\psi} =...

I read somewhere that the error incurred from approximating the Fermi surface to be a sphere in k-space goes as 1/N where N is the number of electrons. So, N is generally of the order 10^23. I couldn't figure out how they came up with the value. I was trying to say that the actual shape of the...

While I understand how the Euler-Lagrange equations are derived by minimizing the integral of the Lagrangian, I don't intuitively understand why Hamilton's principle is true. Specifically, what physical quantity does the Lagrangian represent and what does minimizing it mean? I'd just like to get...

Suppose you are trying the solve the equation of motion of say a particle constrained to move on a surface f(x\vec{},t)=0. The equation of motion is: mx\ddot{} = F\vec{} + N\vec{}, where F is an known external force and N is the unknown constraint force. Now, when you assume that N always...

f and g start out being zero. so because the poisson bracket consists of derivatives of f and g, it need not necessarily be zero even if f and g started off being zero? this is what i would think. but I'm reading a research paper that seems to suggest that if f anf g start off being zero...

Hello, If you have two observables f and g both of which start off as: f =0 and g =0 and you evaluate their possion bracket: {f,g}, will it necessarily be equal to zero? Also, if just f=0 and g wasn't zero, would {f,g} =0? Thanks!

I'm a physics major and I'm pretty sure that I want to go into theoretical physics research. Due to scheduling difficulties and such, I haven't been able to systematically study math. I'm am very comfortable with all the basic math that any physics major should know - multivariable calc, PDEs...

I need to rotate about the origin. I'm not sure what the axis is. Also, tinyboss, I don't quite understand your answer. I know how to do it in 2 dimensions (when theta = pi/2, wheer theta is theta is the polar angle of spherical coordinates - angle made with the z-axis that is). But when...

Anyone? I would really appreciate some help!

Hi, I was wondering whether it's possible to define a rotation in 3 dimensions about the origin. Is it necessary to define an axis of rotation or would it be legal to say that you rotate abput the origin (like a phasor in 3 dimensions.) Thanks!

Hi, I want to rotate vectors through 120 and they are unit vectors so they lie on a unit spheres. So basically the tails of the vectors are at the origin and given one vector with spherical coordinates (1,θ,∅), how do I obtain the coordinates of the unit vectors that make 120 degrees with the...

I'm a physics undergrad and have a GPA of about 3.824/4.3 in an Ivy league university. I have pretty good research experience with 2 publications so far. I was wondering what my chances are of getting into the best grad schools (MIT,Stanford, Caltech etc..) with this GPA, assuming I do fairly...

When you extend the projective line RP1 to the complex half plane, with RP1 as the boundary at infinity, is RP1 the line at infinity for the half plane that we technically cannot "see"? I'm confused about how RP1 fits into the picture of the complex half plane when you make this extension...

Is it possible for two planes to meet in a point instead of in a line?