adapa

I'm no expert but if 2 particles are entangled, then altering the state of one (in an attempt to encode information) would cause it to become disentangled from the other. In other words, the encoded information would not reach the other particle. This makes FTL communication impossible.

I'm a self teacher too. Here is a resource that I find to be useful: http://tutorial.math.lamar.edu/Classes/DE/DE.aspx This one is great for brushing up on the math. If you follow along with the exercises, he makes it very understandable. Pay close attention to the sections on Matrices and Eigenvectors because operators in quantum theory act like matrices on states which are similar to vectors. Also, basis states are similar to unit length eigenvectors. This site also has links to calculus so that you can brush up on integration if you need to. Also as previously implied, Leonard Susskind is an excellent teacher and has some great video lectures on quantum mechanics here :http://newpackettech.com/Resources/Susskind/PHY25/QuantumMechanics_Overview.htm I think that you will get the most out of these lectures if you take ample notes. Also, I find that using the rewind and the pause buttons helps considerably.

Thanks. That makes perfect sense. I am going to try to find some reading on the subject now. It will probably take me a couple of days before I know enough to have any further questions. I sincerely appreciate your help.

Thanks again for answering and please pardon my interrogation. When I had the misconception about the wavefunction being a sum of the products of the eigenstates and their eigenvalues, would it have been more accurate to say that each state is a linear combination of the mutually orthogonal basis states? In other words, when I said that [math]\left|\psi\right\rangle=\sum^{n}_{i=1}C_{i}\left|\phi_{i}\right\rangle[/math] Would it have been more accurate if [math]\left|\psi\right\rangle[/math] is the state, and [math]C_{i}\left|\phi_{i}\right\rangle[/math] is the product of the [math]i^{th}[/math] basis state and its coefficient? Or is this also just as wrong? Thanks again for answering. Pardon the rust.

Thanks for answering. I obviously need to improve my understanding of this part. Also, I have a question about operators. I understand that the operator can be represented as a square matrix. Now is a self adjoint operator described as one where the operator is equal to the transpose of the complex conjugate of itself? Or is that a different concept entirely?

Hi. It's been a couple of decades since I've done anything that is physics related and I am trying to re-activate that part of my brain so please pardon my ignorance if I ask any silly questions. From what I remember, I understand that wavefunctions are represented as vectors in a mathematical manifold called Hilbert Space. I also understand that the wavefunctions are the sums of the products of its eigenstates and their respective eigenvalues, and that these eigenstates are represented as mutually orthogonal unit vectors in Hilbert Space. Is that correct? For example: [math]\left|\psi\right\rangle=\sum^{n}_{i=1}C_{i}\left|\phi_{i}\right\rangle[/math] Where [math]\left|\phi_{i}\right\rangle[/math] represents each eigenstate and C[math]_{i}[/math] represents each eigenvalue on n-dimensional Hilbert Space. So I understand (or at least think I do) that the system is in a state of superposition whenever more than one of the eigenvalues is non zero. I also believe that the wavefunction is considered collapsed when there is only one eigenstate with a non-zero eigenvalue. Is that correct? If not, please feel free to steer me in the right direction. Thanks for answering:-)

Although I am no expert in plasma physics, I am quite fascinated by the topic and I do have some questions. The first question that I have is: Is the temperature of the electrons or the ions in a small volume of an anisotropic plasma better expressed as a rank 2 tensor or a rank 1 tensor (vector) as opposed to a scalar? I know that the magnitude of the temperature should always be a scalar. However, I think that the temperature of the electrons is related to the velocity as in K[math]^{ }_{b}[/math]T[math]^{ }_{e}[/math]=M[math]^{ }_{e}[/math]V[math]^{2}_{e}[/math] Where K[math]_{b}[/math] represents Boltzmann's Constant Because the velocity of the particles in an anisotropic plasma have a directional bias, it would also seem that the temperature would also have a directional bias and give different readings when measured along different axes. If the directional bias favors an imaginary surface, then it seems like a 3 dimensional rank 2 tensor would give the most accurate description of the temperature. I am only asking this because I honestly don't know the answer. Thanks:-)

Hi, I am not an expert in any field (except maybe flying). However, I am quite fascinated by many fields of science and I am interested in learning more.