Wavefunction Definition and 572 Threads

Hello i wonder if anyone here can explain to me, why the wavefunction as a function of position is defined like this: $$\Psi(x,t) = \langle{x}|{\Psi(t)}\rangle$$ Why is it wise to use an inner product as a definition?

I propose a simple thpught experiment; A scientist A measure the spin of an electron and finds it "up". After that he removes all evidence of his experiment and goes away, only to die in a road accident. Another scientist, obviously unaware of the experiment done by A come and measures the...

Homework Statement A wave function is given by: \Psi (x) = a cos(2\pi x) + b sin (2\pi x) for\: x<0 \\ and\\ \Psi (x) = Ce^{-kx} for\: x>0 \\ Determine the constant k in terms of a, b and c using the boundary conditions and discuss the case a >> b. Homework Equations...

If a baryon wavefunction is \Psi = \psi_{spatial} \psi_{colour} \psi_{flavour} \psi_{spin}, and we consider the ground state (L=0) only. We know that the whole thing has to be antisymmetric under the interchange of two quarks. We know that colour is antisymmetric (always colourless) and...

Homework Statement Solve for the wavefunctions and energy levels of an infinite square well potential extending between -L<x<L. Hint: It may be worth noting that for a potential symmetric in x, then the observed probability density must also be symmetric in x, i. |ψ(x)|2 = |ψ(-x)|2. Homework...

I understand that the variational method can give me the "best" approximate ground state wavefunction among the class of the function belongs to. It is the "best" wavefunction in a sense that its energy level is closest to the ground state among its own class. Question: Is it also true that...

Homework Statement The Hamiltonian for a rigid rotator which is confined to rotatei n the xy plane is \begin{equation} H=-\frac{\hbar}{2I}\frac{\delta^{2}}{\delta\phi^{2}} \end{equation} where the angle $\phi$ specifies the orientation of the body and $I$ is the moment of inertia...

Lets say we have a finite square potential well like below: This well has a ##\psi## which we can combine with ##\psi_I##, ##\psi_{II}## and ##\psi_{III}##. I have been playing around and got expressions for them, but they are not the same for ODD and EVEN solutions but let's do this only...

I was reading Penrose's 1968 paper on twistor theory and it seems interesting. Even upon reading around half the paper, I did not find the answer to one of the questions that came to my mind while reading the first few pages. Somewhere in the first few pages (Section 0, 1 and 2), it was...

Problem: Show that \Theta_{20}=\frac{\sqrt{10}}{4}(3cos^{2}\theta-1) is a normalized solution to \frac{1}{sin\theta}\frac{d}{d\theta}(sin\theta \frac{d\Theta}{d\theta})+[l(l+1)-\frac{m_{l}^{2}}{sin^{2}\theta}]\Theta=0 Solution: I know how to show it's a solution, but I'm stuck on showing...

Sometimes we see the wave function broken into specific parts, like $$\psi_{\rm total}=\psi_{\rm space}\psi_{\rm spin}\psi_{\rm isospin}.$$ What determines which parts you include in writing down the wavefunction? For instance, why or why wouldn't we include the isospin part? This has...

All the relevant information about the problem is in the attachment. I just have a problem with the first step, my question it: How is b true? I would have thought that the second part of the exponential function would be taken outside of the integral as well as A since you're taking the...

This isn't a homework question per se but it's a question that I had while reading through my textbook so I think it's appropriate here. I just started studying Quantum Mechanics and so am getting familiarized with the meaning of wave functions and their behavior. One question I can't seem to...

Have you recently came across and remember titles of papers about real experiments concerning the famous double slit electron behaviour? I have found some about electron diffraction, but I'm still looking for those that showed how interference pattern is broken when we watch where the...

Does |\psi(\mathbf{x},t)|^2d^3\mathbf{x} or |\psi(\mathbf{x},t)|^2d^3\mathbf{x}dt give the probability of a particle to collapse at the point \mathbf{x} at time t? Griffiths sides with the former, but I'm having doubts.

I'm currently reading the Griffith book and he dosen't really explain this, do i just miltiply the spin kets with the wave function??

I have seen that the schrodinger wave equation is derived from the assumption that every wavefunction is of the form ψ(x,t)=A(cos(2πx/λ-2πηt)+isin(2πx/λ-2πηt)) where η is the frequency I can understand the real part of the equation. However, I am not able to understand the complex part...

Hey guys, I was reading a book about the philosophy of science, and in the chapter about QM the author uses a well known example in order to explain quantum entaglement and illustrate the non-separability of individual system in QM. He describes a system composed of two spin-1/2 particles...

Homework Statement See the attachment for question and solutionHomework Equations See the hint in the questionThe Attempt at a Solution In part (c), it asks about the probability of finding the particle in ground state. As far as I know, we need to write the wave function in terms of...

As the title suggests, I am interested in symmetries of QM systems. Assume we have a stationary nonrelativistic quantum mechanical system H\psi = E\psi where we have a unique ground state. I am interested in the conditions under which the stationary states of the system inherit the...

Homework Statement The wave function Ψ of a quantum mechanical system described by a Hamiltonian H ̂ can be written as a linear combination of linear combination of Φ1 and Φ2 which are eigenfunctions of H ̂ with eigenvalues E1 and E2 respectively. At t=0, the system is prepared in the state...

A. Given the exact locations of N electrons - can we find out the total wave function and the individual wave functions by some law of nature? B. Given the exact total wave function - can we find out the coordinates of each electron and the indiviual wave function of each electron by some law...

Homework Statement Given the wavefunction, \psi(x) = Cx for 0 < x < 10 and \psi(x) = 0 for all other values. What is the normalization constant of C? I got \sqrt{3/1000}. What is <x>? I got 30/4. What is <p>? Here is where I'm confused.Homework Equations \langle p \rangle = C^2...

Homework Statement Show that ψ(x) = Acos(kx) is not an eigenfunction of the momentum operator. If you were to measure the momentum of a particle with this wavefunction, what possible values would you get and what would the probability be of obtaining these values? Homework Equations...

Basically, the problem gives me a wave function and asks me to find the wave function in momentum space. It then asks me to find the expected value. Namely <p> and <p^2>. The problem is, when I try to calculate <p> it blows up to infinity. What am I doing wrong? Here is my work...

Neumann's Principle states: If a crystal is invariant with respect to certain symmetry elements, any of its physical properties must also be invariant with respect to the same symmetry elements. So, does this apply to the wavefunction of an electron in a crystal? Or, stated another way, if...

how is the wavefunction of 1-D infinite well modified by the application of an electric field to the well.

Homework Statement Suppose that there is a wavefunction \Psi (x,0) where 0 is referring to t. Let us also say that a(k) = (C\alpha/\sqrt \pi )exp(-\alpha^2k^2) is the spectral contents (spectral amplitudes) where k is defined as wavenumber k. \alpha and C is some constant My question is, why...

Hi there! I have tried to apply time reversal (which makes t -> -t) to a free particle wavefunction: Exp[i(p.r-Et)/\hbar] and got: Exp[-i(p.r-Et)/\hbar] I got this by flipping the sign of p since it has a d/dt part, and flipping the t in the Et part. However I think this is wrong...

All I need to evaluate the normalization coefficient. I need a step by step guide. It will be a great help if someone please tell me where can i get the solution (with intermediate steps). I think the solution can be done using the orthogonal properties of associated Laguerre polynomial. I need...

So, in QM making a measurement collapses the state into an eigenstate of that observable. Thus, if the system is properly isolated, then the same measurement should return the same value. But the eigenvalue for that state is degenerate, then does that mean the state might actually collapse to a...

Hi! I'm currently re-reading Griffiths introductory QM book and plan to do most of the exercises. I got stuck on one problem and had to look for some hints and found two solutions that both claim that: \int_{-\infty} ^{\infty} \frac{\partial }{\partial x}\left[ \frac{\partial \Psi...

I was wondering why is the nucleus willing to confine itself in one place while the electrons are free to appear anywhere around the nucleus within the orbital. Electrons have this wave function, is there one for the nucleus?

The wavefunction is defined on the domain of complex numbers. To find the probability of discovering a particle in a certain region, the amplitude of the wavefunction is integrated over that region. The problem is that you have an infinite set of complex numbers mapping to a single amplitude...

Homework Statement Find the constant A such that the equation \psi(r,\theta,\varphi)=\sqrt{6\pi}A\sqrt{r}e^{-r/a} Wich describes one electron in a hydrogenatom, is normalized The Attempt at a Solution I figured this equation is seperable in the form...

I am having troubles finding anything online that reveals the conceptual concerns relating to the probability wavefunction in regards to the travel of a particle and then how that plays into the double-slit experiment. No math is required. I merely need to know the concepts involved. 1) exactly...

This question is not directly related to QM although my reason for asking it is I'm trying to compute wavefunctions on my PC -- please excuse me if this is the wrong place to ask. I am having trouble using the DFT in Mathematica although I don't think my problem is directly Mathematica related...

Forgive me for asking such a basic question but say for IDSW1 if we have a wavefunction that is a superposition of the first two energy eigenfunctions so: ψ(x)=(1/√2)*(ψ1+ψ2) then if we measured say E1 we can eliminate the inconsistent part of the wavefunction so the wavefunction collapses to...

My first response to the question is "No", since electron and positron are distinguishable by their charge, so it's not necessary the wavefunction remains the same(up to +/-) upon permutation of particles. However on second thought, in the quantized Dirac field electron and positron creation...

Hey, I have been churning the idea of Dirac notation around in my head and I am thinking about the position and momentum basis representation of a wavefunction in a Hilbert space. Wikipedia mentions the following in the article 'Bra-ket notation' under the heading 'Position-space wave...

Homework Statement Assuming the five basis atomic orbitals are normalised use the Huckel approximations to normalise the wavefunction for the cyclopentadienyl radical Wavefunction = \phi_{1}+\phi_{2}+\phi_{3}+\phi_{4}+\phi_{5} . Homework Equations I know that \phi_{i}\phi_{j} = 1 if...

I've read that color was introduces as a degree of freedom nessecary to satisfy the pauli exclusion principle in the quark model of particles. For example for the omega minus which had an observed total spin of 3/2 and no angular momenta ment that the spin had to the the same for all of the...

Hi! I've read a lot of posts about the photon wavefunction. I'd like to ask you if this statement is correct: "It is possible to write down a wavefunction for the photon which correctly describes its dynamics. But this wavefunction cannot be interpreted as an object whose squared modulus...

So I bugged the folks in General Physics about the latter form of the question a while back, and got some rather unconvincing "can't be done" replies. To state the problem specifically (and my motivation): Let's say that the probability density of finding a particle at any place/time is given...

Hello, destructive interference seems like an important part of quantum physics, but I'm finding it very hard to grasp it conceptually. For instance in the Elitzur–Vaidman bomb tester, destructive interference in the mirror is used to determine if one of the paths is blocked. What exactly is...

What is the physical basis for the requirement that the wave function has finite and continuous first order derivative?

Homework Statement Consider the nonstationary state: \Psi = \sqrt{\frac{1}{3}}\Psi_{22-1} + \sqrt{\frac{2}{3}}\Psi_{110} Where \Psi_{22-1} and \Psi_{110} are normalized, orthogonal and stationary states of some radial potential. Is \Psi properly normalized? Calculate the expectation value of...

Homework Statement Consider any ket. Find the perturbative correction to that ket. Then, |n> = |n0> + |n1> Here, |n0> is the ket from the unperturbed hamiltonian (who cares what it is), and |n1> is the 1st order correction. Do you introduce a new normalization when you add the...

I see why having mutiple points of infinity in the wavefunction would be bad. But what about one point being infinity and everywhere else being zero? Is this the only case where the wavefunction could have an infinite value? Would this be a case where the expectation value of whatever...

Homework Statement The wavefunction describing state of a system is, \psi (r,\theta ,\phi )=\frac{1}{8\sqrt{\pi }}\left( \frac{1}{a_{0}}% \right) ^{3/2}\frac{r}{a_{0}}e^{-4/2a_{0}}\sin \theta e^{-i\phi } Find the parity of system in this state. The Attempt at a Solution \psi...