Qm Definition and 1000 Threads

For those of us trapped in a corner with difficult choices of whether to believe many worlds are splitted off billions of times every second or whether there is Godlike power to collapse the wave function in the universe or whether waves can travel forward or backward in time (Transactional) or...

I'm a junior undergraduate who has yet to take quantum mechanics, although I did have a brief introduction to basic wave mechanics (square well, harmonic oscillator, tunneling, the hydrogen atom, etc.) in "modern physics" course. I've also watched and taken notes from the Quantum Mechanics...

I just finished a course on linear algebra. The class was quite slow, and not much material was covered (essentially going as far as diagonalization w/ some applications). Seeing as I will be taking a QM course next semester, I thought that it might be a good idea to advance myself on the math...

.. This thread is intended to focus on arithmetic issues, mainly raised by JesseM, vanesch, DrChinese, ThomasT, in the context of: "What's wrong with this local realistic counter-example to Bell's theorem?" https://www.physicsforums.com/showthread.php?t=475076 : For newcomers to the issues...

.. In his text-book "Quantum Theory: Concepts and Methods", Asher Peres (1995) writes: A: "Bell's theorem is not a property of quantum theory." - (p.162, Peres' emphasis). B: "This conclusion can be succinctly stated: unperformed experiments have no results." - (p.168, Peres' emphasis)...

The commutator for group theory is [X,Y]=X^{-1}Y^{-1}XY whereas the quantum commutator is [X,Y]=XY-YX . At first glance, the two commutators seem to be totally unrelated because the quantum commutator speaks of two binary operations whereas group theory has one binary operation. However...

Hello, I am trying to express a given wavefunction through different basis, momentum and position. Look at 5.2(b) and (c) through the link: http://qis.ucalgary.ca/quantech/443/2011/homework_five.pdf" I complete part (b) by doing the following...

I'm am trying to derive the relations: a|n\rangle=\sqrt{n}|n-1\rangle a^{\dagger}|n\rangle=\sqrt{n+1}|n+1\rangle using just the facts that [a,a+]=1 and N|n>=|n> where N=a^{\dagger}a (which implies \langle n|N|n\rangle=n\geq 0). This is what I've done so far: [a,a^{\dagger}]=1 \Rightarrow...

Someone posted this on another forum, and, not knowing enough about it to supply a satisfying answer, I figured I'd ask you guys.

Hi! I'm struggeling with a quantum mechanical problem. Homework Statement An alpha-particle is "trapped" inside a uraniumcore, and the potential is simplified to 0 for R2 < r V0 for R1<= r <= R2 0 for 0<= r < R1 I have calculated the transmission coefficient T =...

Homework Statement Hi Say I have an operator O, and I find its expectation value <O>. Now, if I wish to find the expectation value of O† († denoting Hermitian conjugate), then will this just equal the complex conjugate of <O>? Niles.

hello, can anyone please share the name(s) of the qualified textbooks for QM? thanks in advance..

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 I'm trying to derive the second-order correction of energy in time independent perturbation theory. My professor did it the Landau's way so I'd rather use his notation (without bra and kets). I already derived the first-order correction: E_n^{(1)}=V_{nn}=\int...

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...

Homework Statement Consider free space (V (x) = 0 for all x). For the state function \psi(x, t = 0) = exp(ikx) + exp(i\varphi)exp(i2kx) where \varphi is some arbitrary real constant, determine (x, t) for t > 0, and (ii) the probability current density (as a function of x and t)...

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...

Homework Statement Hi guys Ok, I have some questions, which I would very much like for you guys to help me with. Say I have some state |1>, which denotes the first, n=1, solution of the infinite, square well. |1> is a vector in the Hilbert space spanned by all the eigenvectors of the...