Qm Definition and 1000 Threads

I collect here info from another thread, to have a more focussed discussion. ''this particular assumption'' refers to the assumption that |psi(x_1,...,x_n|^2 is the probability density of observing simultaneously particle k at position x_k (k=1:N). Please show me a comparison with experiment...

I'm looking for a summary of what invariance or symmetry of the Action in Feynman's path integral has on the equations of motion and on measurement. Do different symmetry groups of the Action integral result in different equations of motion for different particles? Is the least action principle...

Please teach me this: Why discontinue(quantum) characteristic ultimately relates with probability characteristic in Quantum Mechanics(and Quantum Field Theory).It seem to me the discontinue spectral of an observation correspond with a ''integral measure'' of a type of integral.So the...

I always hear that these two things are incompatible but I never really hear why. The most I know is that QM assumes a quantized spacetime whereas GR assumes a dynamic one, but I don't really understand if this is correct (nor do I get what that really means). I don't see how GR would fail...

Correct me where I go wrong. I understand two particles can not share the same quantum numbers, but electrons in separate atoms do share the same quantum numbers. Where's the limit? How far away from a particle do you have to be in order to be able to consider that state "empty"? Thank...

When we talk about "Hilbert space" in (undergraduate) QM, we are typically talking about the space of square-integrable functions so that we can make sense out of \int_{-\infty}^{\infty} |\psi(\vec r,t)|^2 d^3x. But are we talking about Riemann-integrable functions or Lebesgue-integrable...

In Stress Energy Tensor the following components make sense to me: Energy density, Momentum Density, Energy flux because they are based on the 'observables' Whats about the Pressure? What is it (microscopically)? On the microscopic level there are 'particles' flying in different...

Most people on this forum know the basic theory of black hole formation. When a massive star runs out of fuel there is no longer enough heat pressure pushing out against the gravity pulling in and the star collapses. The density of the core and resulting remnant become so large that nothing, not...

Homework Statement The unperturbed Hamiltonian H0 of two independent one-dimensional operators is H_0=a^{\dagger}a+2b^{\dagger}b where a and b are operators such that [a,a^{\dagger}]=1=[b,b^{\dagger}] Find the degeneracies of the eigenvalues of H0 with energies E0 = 0, 1, 2, 3, 4...

Hi, I came across the following expression in Landau and Lifgarbagez's Quantum Mechanics (Non-relativistic Theory) book: \left(\cos\theta\frac{\partial}{\partial r} - \frac{\sin\theta}{r}\frac{\partial}{\partial\theta}\right)R_{nl}(r)Y_{l0}(\theta,\phi) =...

Can I draw conclusions from the curvature of a wavefunction on the kin. energy of the particle? For instance, the lowest bound solution of a particle in the box is a half of sinus: Psi(x) = sin(pi*x/L) Since the second deriv. of a wavefunction is proportional to the kin. energy, this would...

Homework Statement Please see attached problem Homework Equations The Attempt at a Solution Ok so I am just stuck on the bit that asks us to write down the appropriate form of the interaction hamiltonian H int for two oscillating particles connected by a weak spring. Is it 1/2...

Supposed external energy is added to the system such that the electron is rise to the next orbital releasing photon. Can QM still be used to model it or does one need Quantum Field Theory? How about additional external energy that increase say the molecular rotational or translational speed, is...

I was wondering whether anyone knows of any downloadable or web-based applications that are geared toward theoretical and quantum mechanical physics equations. My IDEAL program would have: -The ability to solve and graph equations from quantum mechanics and theoretical physics (such as Loop...

Homework Statement Problem 2.11 of Liboff's Introductory Quantum Mechanics, 1st edition Suppose that you are inside a blackbody radiation cavity which is at temperature T. Your job is to measure the energy in the radiation field in the frequency interval 10^{14} to 89 \times 10^{14}...

Hello, I am trying to decompose |(pi/2)+\vartheta> into canonical basis. I have done it for |\vartheta> but i am unsure about what to do with the pi/2. Given |theta> = (cos\vartheta sin\vartheta) I was thinking that pi/2 becomes (0 i) and I would add the two vectors together. Any help would...

I'm reading this: ==quote== Einstein's theory of gravity, General Relativity, and our theory which governs the sub-atomic world, Quantum Theory, give seemingly inconsistent accounts of the nature of time. According to General Relativity, each observer will have a separate notion of time...

Homework Statement Let H= \frac{1}{2}m(V_x^2+V_y^2+V_z^2)+u(\vec{Q}) be the hamiltonian operator for a particle which has mass m>0 with u(\vec{Q})=\lambda_0 (Q_x^2+ Q_y^2). Knowing that [Q_\alpha, m V_\beta]=i \delta_{\alpha \beta}. Show that If \displaystyle A_\alpha= \frac{d...

Hello fellow physicists! I'm currently trying to learn some QFT and the reader gives an introduction by expressing the non-relativistic hamiltonian with integral and creation, destruction operators. Later he writes: |Psi, t > = \int d3x1...3xn Psi(x1, ..., xn; t) a+(x1) ... |0> And...

Homework Statement The vector |p> is given by the function x+2x2 and the operator A = 1/x * d/dx, with x = [0,1]. a) Compute the norm of |p> b) Compute A|p>. Does A|p> belong to the VS of all real valued, continuous functions on the interval x = [0,1]? c) Find the eigenvalues and...

Homework Statement A system at time t = 0 is in the state |ψ> = a|E1> + b|E2>, where |E1> and |E2> are (normalised) energy eigenstates with two different energies E1 and E2, and a, b are real numbers. Write down the state |ψ, t> for the system at time t. What are the probabilities at time t to...

When you square the probability amplitude and it shows there is 20% probability of it occurring, and you perform the experiment 100 times.. you would find exactly 20 times as dictated by the probability. In radioactive decays, individual alpha particle may tunnel at different times but when you...

I just transferred to Georgia Tech from Georgia State and I'm registering for classes. I ave taken Intro Phys 1 and 2, and intro to modern physics. I have math up to DE. I will be taking Classical Mechanics this semester, and am wondering if it is a good idea to take QM before completing the...

And it has one of the largest physics+astrophysics undergraduate enrollments in the nation. Will graduate admissions committees know about this? Especially if they have many applicants from my school? Will this devalue a high grade in that QM course?

I am working my way through Ballentine's Quantum Mechanics and I am stuck on the following problem. Homework Statement Problem 3.1 from Ballentine: Quantum Mechanics Space is invariant under the scale transformation x\to x'=e^cx where c is a parameter. The corresponding unitary...

Hey everyone, I'm a physics major in junior year that missed out on my classical mechanics class this fall semester because of some prereq stuff. I emailed the professor teaching QM next semester and got in without the necessary classical prereq. He said I should go over "the Hamiltonian and...

Is there anyone on the forums that does research in QM or QFT? I ask because I find this area of physics very interesting at least to read about, and I enjoy challenging mathematics. While I am still only at the freshman/sophomore level in my physics education, I have always been interested in...

Homework Statement A beam delivering protons is sent through a stern-gerlach splitter oriented to ask whether the spin is oriented parallel to the y axis. What fraction of protons have spin down with respect to the y axis? \chi=\stackrel{1}{\sqrt{17}} \stackrel{4}{i} the 4, i thing is the...

I know that in QM, one observation like position will alter the wavefunction so that momentum changes. But how do we see this mathematically when we include time dependence, whether in matrix mechanics or wave mechanics? Is it as simple as writing PQx where x is the state, Q position matrix, P...

I don't really get the part that we shouldn't "imagine" quantum mechanics .I mean, I know what eigenvectors are in three dim for a known operator and I know what's the meaning of uncertainty that u can't know the place of any particle unless u look, and when u look, means u have to hit it by...

Homework Statement Hi Say I have the following number: \left\langle {\psi _i |A|\psi _j } \right\rangle 1) First of all, am I correct when saying that \left\langle {\psi _i |A|\psi _j } \right\rangle = \left\langle {\psi _j |A^\dag |\psi _i } \right\rangle ^* where...

Homework Statement Introduction to Quantum Mech Griffiths 4.9for the problem of a finite square well v(r) = {-Vo r<= a (i will call section I) 0 r>a (section II)Homework Equations After I find uI and uII uI = A sin(K r) uII = De^-kr and then set the boundary condition uI =...

Hi, In QM symmetries can be represented by unitary operators. For example for rotations: \hat{U}_{R}\psi(\vec{x})=\psi(R^{-1}\vec{x}) , which is simple enough, as it just says that the vale of the rotated wavefunction at some point is the value of the old wavefunction at the pre-rotated...

Homework Statement Q:The bond between the hydrogen and chlorine atoms in an HCL molecule has a force constant of 516 N/m. Is it likely that a HCl molecule will be in its first excited vibrational state at room temp? When doing my HW, I always check my answers against the solutions...

The phase of a pure momentum state for a single particle traveling freely is (p.r – Et) / h-bar. This also happens to be the Minkowski space-time dot product of the 4-momentum and the space-time 4-vector (relativistic action). Is that just a coincidence or is phase inherently...

Hi guys I am reading a book, where they use vector expressions a lot. In it they write {\bf{M}} = \sum\limits_{\psi ,\psi ',\sigma ,\sigma '} {\left\langle {\psi '} \right|\left\langle {\sigma '} \right|{\bf{m}}\left| \sigma \right\rangle \left| \psi \right\rangle a_{\psi ',\sigma '}^\dag...

Homework Statement Hi guys As we have discussed earlier, we can represent some operator in an arbitrary basis by the use of the 1-operator: T = \hat{1} T \hat{1} = \sum\limits_{\sigma_a,\sigma_b } {\left| {\psi _{\sigma_a} \left( {r_i } \right)} \right\rangle...

In thermodynamics, two variables A and B are uncorrelated when: <AB>=<A><B> where <> are the expectation values in thermodynamics (for example calculated using Boltzmann distributions). What are the conditions in quantum mechanics for two operators to be uncorrelated, i.e...

I'm pretty confused by the rules regarding the total energy, the kinetic energy, and potential of a QM system. Does the total energy have to be positive or greater than zero? And if so, why not? I don't really understand what it means to have a negative total energy of a system I guess. I...

Hey, I am a second year physicist, and I have only recently been introduced to the postulates of QM. I am still trying hard to understand how the original inventor's of QM came up with the third postulate. Postulate 3 says the classical combination of dynamical variables gives the correct...

Homework Statement Hi Say I have the kinetic energy operator denoted by T(ri) for the particle i. I wish to represent it in some \left| \sigma \right\rangle -representation. My book says it is given by T = \sum\limits_{\sigma _a ,\sigma _b } {T_{\sigma _a ,\sigma _b } \left| {\psi...

Why do we have to use operators in QM?

Hi all, Please can you suggest a good book of quantum mechanics?

I should know how to do this, but I've been getting a bit confused. Can you solve the particle in a box problem considering that the particle is a massless photon? I'm not so sure on how to write the Hamiltonian correctly for this problem. EDIT: Ok, to add some information, I'm actually looking...

Homework Statement This is a quick one, which I apologize ahead of time for not writing this out more neatly. The parentheses denote subscripts. I have a system of two particles, which are in a superposition Psi(one) + Psi(two). The energy of particle one is E(1) and of particle two is...

Is QM really applicable to everyday life in the macrocosm? If it is, how? And does QM say there are no causes, only effects. So, for example, in th e real world (macrocosm), there is a set of possibilities A, B, and C, and causal factors x, y, and z. However, x is an unknown or hidden...

Hi, As I'm sure you are all well aware, QM is all about probability in your measurement. When we scale up to the classical world, the probabilities disappear, we calculate one specific state for your system given a certain set of starting conditions. What I was wondering is, is the QM world...

Homework Statement Pro #2 if you click on this link. http://s1104.photobucket.com/albums/h332/richard78931/?action=view&current=hw4.jpg Homework Equations , The Attempt at a Solution Click here http://s1104.photobucket.com/albums/h332/richard78931/?action=view&current=2a.jpg...

Homework Statement A free particle at time t=0 has the Gaussian wave-packet: \Psi(x,t=0)=Ae^{-\tfrac{x^2}{2\sigma^2}}e^{ik_0x} (a) What is A? (b) What is the probability of measuring a momentum in the range between p and p+dp? Homework Equations (a) \int^{\infty}_{-\infty}|\Psi(x,t)}|^2...

Hello all. As I understand it, there's somewhat of a divide in the scientific community (basically between chemists and physicist) around the topic of solutions to the SE (or KS eqn) that give fractional occupations of molecular or KS orbitals. I myself see no physical reason why probability...