# Tagged Questions

A complex scalar field that describes a quantum mechanical system. The square of the modulus of the wave function gives the probability of the system to be found in a particular state.

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### Is the free electron wavefunction stable?

The wavefunction of a free electrons is variously described as a plane wave or a wave packet. I am fairly happy with the wave packet, as it is localised. But if we change to the electron's rest ...
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### State of a system in Quantum Mechanics and state vectors

I'm taking a course in Quantum Mechanics and there is something I'm not being able to fully understand. On more elementary courses on Quantum Mechanics I've been told that the idea of Quantum ...
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I've been solving a problem in quantum mechanics, and I was deriving the standard deviation of $P$, knowing that $\langle P\rangle=0$. Because $\Delta P=\sqrt{\langle P^2 \rangle - \langle P \rangle ^... 4answers 380 views ### Does$\lvert\langle p\lvert\psi\rangle\rvert^2$have any meaning at all? I used to think$\lvert\langle p\lvert\psi\rangle\rvert^2$had the meaning of some likelihood of the particle's momentum being$p$(within some tolerance interval$\Delta p$). Now I'm just confused. ... 5answers 688 views ### How does a Wavefunction collapse? I have been wondering and researching... How does a wavefunction collapse into one state?More specifically, what conditions cause a wavefunction for a quantum particle to collapse? Does this have to ... 1answer 653 views ### Help me understand the first equation in Landau & Lifshitz's Quantum Mechanics While I've covered a basic course in Quantum Mechanics, I'm self-studying Landau & Lifshitz's book to help me understand what's going on. Unfortunately, I'm stuck on the very first equation in ... 3answers 2k views ### Born Interpretation of Wave Function I have just started Griffiths Intro to QM. I was studying Born's interpretation of Wave function and it says that the square of the modulus of the wave function is a measure of the probability of ... 1answer 3k views ### 3D Quantum harmonic oscillator For an isotropic 3D QHO in a potential $$V(x,y,z)={1\over 2}m\omega^2(x^2+y^2+z^2).$$ I can see by independence of the potential in the$x,y,z$coordinates that the solution to the Schrodinger ... 4answers 206 views ### Isn't the 'slit' in a double-slit experiment also a wave? I'm new to QM so excuse my naivety. I was watching an online MIT QM course that described the double-slit experiment (with electrons) when it occurred to me that I have a question. In the video, the ... 2answers 2k views ### Linear vs. quadratic dispersion relation In wave mechanics the dispersion relation between frequency$\omega$and wave number$k$is linear: $$\omega_n=c k_n$$ But in quantum mechanics, based on Schrödinger's equation, one can show that we ... 1answer 87 views ### Why can we leave off half of the general solution? In these pdf notes, it says at the bottom of the first page and beginning of the second: [...] whose solution is: $$\Psi(\theta) = c_1 e^{i\omega\theta} + c_2 e^{-i\omega\theta}$$ Since we are ... 2answers 271 views ### What is the physical reason behind linearity of Schrodinger's equation? What is the physical reason for Schrodinger equation to be linear? Though in physics many interactions or dynamics are found non linear. 3answers 244 views ### Can a wave possess spin? Since a matter wave is associated with a particle in quantum mechanics, does the wave spins? I mean, can we visualize the spinning of wave or is it possible that the wave spins? 3answers 1k views ### Comparison of 1D and 3D wave functions When discussing the Schroedinger equation in spherical coordinates, it is standard practice in QM handbooks to point out that the radial part of the 3-dimensional wave equation bears a strong analogy ... 2answers 339 views ### A quantum particle which is almost at rest but whose position is random! Assume a particle is given by a quantum state which is constructed in such a way that it is equally probable to find it anywhere in an fixed interval$(0,L)$but has arbitrarily low velocity. The ... 2answers 225 views ### Born Oppenheimer Approximation: Why can any molecular state be represented as a linear combination of electronic states? in the Born Oppenheimer Approximation, one expands the molecular wavefunction$\Psi(x,X)$in terms of the electronic wavefunctions$\phi(x;X)$: $$\Psi(x,X)= \sum_k(c(X)_k\phi(x;X)_k)$$ ($x$are the ... 4answers 4k views ### Why is wave function so important? I am almost sure that the wave function is the most important figures in modern physics book. On the other hand I know that wave function even do not have a physical meaning it self alone! Why is ... 2answers 993 views ### Where does the wave function of the universe live? Please describe its home Where does the wave function of the universe live? Please describe its home. I think this is the Hilbert space of the universe. (Greater or lesser, depending on which church you belong to.) Or maybe ... 1answer 101 views ### Dirac Equation in RQM (as opposed to QFT) is written in which representation? In introductory Quantum Mechanics treatments it is common to see the Schrödinger's equation being written, simply as: $$-\dfrac{\hbar^2}{2m}\nabla^2\Psi(\mathbf{r},t)+V(\mathbf{r})\Psi(\mathbf{r},t)=... 2answers 92 views ### Is \phi_n =\left\langle \vec r | n \right\rangle the photon wave function? I am a bit confused about this issue and I am still not clear whether is there is a photon wave function or not. Since we use Fock states | n \rangle to represent the state of a quantized ... 2answers 515 views ### Why does \ell=0 correspond to spherically symmetric solutions for the spherical harmonics? In quantum mechanics why do states with \ell=0 in the Hydrogen atom correspond to spherically symmetric spherical harmonics? 3answers 890 views ### Historical background of wave function collapse I wonder what were the main experiments that led people to develop the concept of wave function collapse? (I think I am correct in including the Born Rule within the general umbrella of the collapse ... 1answer 1k views ### Confusion between the de Broglie wavelength of a particle and wave packets So I learned that the de Broglie wavelength of a particle, \lambda = \frac{h}{p}, where h is Planck's constant and p is the momentum of the particle. I also learned that a quantum mechanics ... 1answer 116 views ### In interpretations of QM where the wave function is real, what does that mean? In a lot of interpretations of Quantum Mechanics they believe that the wave function is "real". But what does that mean? Are they saying that the wave function of an elementary particle (electron/... 2answers 118 views ### Do quantum wave functions curve spacetime before they are measured Do wave functions cause spacetime curvature before they are measured, or would curvature only happen upon measurement? I guess the question becomes, do quantum wavefunctions carry energy while they ... 1answer 135 views ### Orbital angular momentum of electrons In a QM class, to study the hydrogen atom, we started by defining the Hamiltonian H for a central potential, then made an orbital angular momentum operator appear as part of H, then down the line ... 4answers 541 views ### Projection of wavefunction onto basis function I am given to believe that one way that one would could represent a wavefunction is by the expansion$$\Psi(x) = \Sigma_n \Psi_n(x) = \Sigma_n f_n\phi_n(x) \tag{1}$$where$\{\phi_n (x) \}$is an ... 1answer 926 views ### Orthogonality of summed wave functions Problem. I know that the two wave functions$\Psi_1$and$\Psi_2$are all normalized and orthogonal. I now want to prove that this implies that$\Psi_3=\Psi_1+\Psi_2$is orthogonal to$\Psi_4=\Psi_1-\...
I am confused with connection between state $| \psi \rangle$ of a quantum system and corresponding wave function $\psi(x)$ (at a given time). I have been told that for every state $| \psi \rangle$ we ...