Wavefunctions Definition and 146 Threads

Why do wavefunctions in quantum mechanics need to be complex? What are the drawbacks of using real valued wavefunctions like: Asin(kx+ωt+ø) etc...or a standing wave equation: Asin(kx)cos(ωt)? I'm an undergraduate student and recently passed 12th grade...So any answer of my level would be...

Maybe someone here can explain me something I never understood in QM: The wave function lives in the Hilbert space spanned by the measurement operator. Is there any mathematical relation of those spaces with each other?

Homework Statement Find the eigenfunctions and the eigenvalues of the following Hamiltonian \hat{H} = \frac{1}{2m} \left ( \frac{ \hbar}{i} \vec{\nabla}-\frac{q}{c}(0, B_z x,0) \right ) ^2 = \frac{1}{2m} \left ( - \hbar^2 \vec{\nabla}^2-\frac{\hbar q}{ic}(\vec{\nabla}·(0, B_z\hat{x},0) +...

I know about symmetry and antisymmetry and so on, but a thought that I had never considered just hit me. If we had two fermions in the triplet symmetric spin state and hence therefore an antisymmetric spatial state, for example a harmonic oscillator in the first excited state must be one in...

There are many cases, for simplicity, we choose the wavefunctions to be real. For example, in http://en.wikipedia.org/wiki/Born%E2%80%93Oppenheimer_approximation, there is "The electronic wave functions \chi_k\, will be taken to be real, which is possible when there are no magnetic or spin...

Hi. I've been learning quantum mechanics from different sources and I'm starting to notice that they have really different ways of treating certain things. For example: in some places Griffiths works with wavefunctions, while Sakurai works using eigenkets. This confuses me. As I...

Homework Statement What quantum numbers are used to define state of hydrogen? The wavefunction has no angular dependence. Find the values of all the angular momentum quantum numbers for the electron. Homework Equations The Attempt at a Solution The numbers are n, l and m. n: Energy level...

Homework Statement So I was able to find a problem that was kind of similar to a homework problem that I am working on. Unfortunately, I'm not quite sure what is going on partially within the problem. In the problem they state that \phi=\phi*, but it does not state why. I was wondering...

Homework Statement The equation \psi(x) = \frac{1}{sqrt(2)}\psi_0 (x) + \frac{i}{sqrt(5)}\psi_1 (x) + \gamma\psi_2 (x) is a combination of the first three eigenfunctions in the 1D harmonic oscillator. So, \psi_0 = Ae^{-mωx^2 /2\hbar} and so on for the first and second excited states. If...

In my electronics engineering program, we have topics on quantum mech, statistcal mech and so on(only intuitive treatment, not mathematical)...We follow'Introduction to modern physics' by Sir Arthur Beiser. I have a small doubt in the wavefunction of a system.. Let a system consist of two...

Hi Folks -- can anyone direct me to a table online which lists the wavefunctions for the hadrons in terms of their constituent quarks? (I'd like to look at how the wavefunctions can differ even for particles with the same quark content.) Thanks a lot!

Hi I was learning about eigenvectors, inner products, Dirac notation etc. But I don't get why wave functions are represented as eigenvectors?

In our physics class of quantum mechanics, we constantly talk about normalisation and normalising wavefunctions such that the total probability of finding the particle in infinite space is one. I don't get why do we normalise and how do we normalise(I have not taken up statistics course). It...

Hi, I've been thinking about the following scheme: let's say I have an incoming photon ray with wavefunction ψ1 that finds a bloch electron with wavefunction ψ2. Is there any way to compute the optical coefficients (transmitivity, reflectivity etc) of the material knowing only this two ψ and...

Consider an electron in a periodic potential V(x) such that V(x+a) = V(x) for some real number a. The energy eigenstates are obtained from time-independent SE, which in atomic units is -\frac{1}{2}\frac{\partial^{2}\psi(x)}{\partial x^{2}}+V(x)\psi(x)=E\psi(x) According to Bloch theorem, the...

Hello, Wave functions and energy levels... What particles are being described by Schrodinger's equation? If we are talking about energy levels, do we mean the energy levels in an atom? Other particles, such as electrons or quarks... do they have energy levels, or are they too small for us to...

Homework Statement Consider a particle in an infinite square well described initially by a wave that is a superposition of the ground and first excited states of the well ψ(x,0) = C[ψ_{1}(x) + ψ_{2}(x)] Show that the superposition is not a stationary state, but that the average energy...

Two related questions: (1) The wavefunction is characterised as encoding all the physical characteristics of a particle. But which ones? The quantum numbers? In that case, since each quantum number ranges over discrete values, there would seem to be only a countably (as opposed to a continuum)...

Hi, Homework Statement A quantum harmonic oscillator is in a superposition of states(below): \Psi(x,t) = 1/\sqrt{2} (\Psi_{0}(x,t) + \Psi_{1}(x,t) \Psi_{0}(x,t) = \Phi(x) * e^{-iwt/2} and \Psi_{1}(x,t) = \Phi_{1}(x) * e^{-i3wt/2} Show that <x> = C cos(wt) ...Homework Equations Negative...

(The following is a purely qualitative consideration of Quantum Mechanics) In a particular Quantum Mechanics text, I've come across the following quote which I'm having some difficulties interpreting. "We describe the instantaeous state of the system by a quantity \Psi , which satisfies a...

Please I need help with wavefunctions! Okay so I have attempted to understand wavefunctions in my pchem class but I am a little lost... Here is the problem. unnormalized wavefunction (ψ) = e^(iψ) with 0≤ψ≤2∏, normalize this equation Homework Equations N^2∫ (ψ)^2 dψ **I uploaded a...

Hey My question is displayed below I think I have done this right but I wanted to check, we have to normalise the wavefunction first and I think this is done by assuming each state is equally likely and so assigning some constant 'c' to premultiply each of the 3 states. We need...

I have a quantum problem that I can't seem to figure out: There's an electron in a 1-D rigid box of length 2A but it is known to reside in a central segment of 1A with uniform probability of residing within this segment. There are two possible wavefunctions: one with constant phase...

This is what is bugging me at the moment: What determines if a particle striking another particle will become a combined wavefunction of probabilities or both of them will collapse, is it probabilistic weather it combines or collapses? I also heard scientists were able to create an atom on...

Homework Statement Given state: |ψ> = |0> + α|1> + σ^2/√2 |2> find the wavefunctions. I am confused between states and wavefunctions, everywhere I've read it says that state (ie the wavefuctions), really need some enlightenment here..

Homework Statement Consider a particle in a 2nm sphere with infinite potential energy outside and zero potential energy inside the sphere. Calculate the energy of the following wavefunctions: 1s, 2p, 3d Homework Equations H(hat) = p(hat)^2/2m(sub zero) + V(r) V(r) = ∞ when r ≥ 2 nm...

Homework Statement Is it possible given a wavefunction ψ(x,t) to find the probability that the particle is at a particular location over an interval of time? Homework Equations The Attempt at a Solution Intuitively, given that the probability of finding the particle in a region...

Dear all, I have a quantum system made up of two layers. An electric field is applied with two voltages applied at both layers. I want to calculate the electronic densities that reside at the two laters in terms of the wavefunctions obtained from solving the HamiltoniaN..Anyone knows of an...

'If particles also behave as waves, then what is oscillating?' I'm fairly sure that most people would consider this a nonsensical question. But I'm not sure why and I was hoping someone could clear this up for me. My thoughts are: The wave function is just a mathematical model, so don't...

I am reading the fine structure article from Wikipedia at http://en.wikipedia.org/wiki/Fine_structure. Under the heading 'Kinetic energy relativistic correction', we have the following: For the hydrogen atom, V = e2/r. This implies that the expectation of V = -e2/a0n2. Now, I know that...

this reminds me of a question that I'd like to ask. as a chemist, my view of quantum mechanics is that it is a useful tool to give the right answer for spectroscopy calculations and to make a model of complicated molecules so that we can pin down some parameters with instruments, then get the...

[SOLVED] Superposition of two wavefunctions Homework Statement The problem is more of complex number arithmetic more then conceptual : Homework Equations |\psi|^{2}=\psi\psi^{*} The Attempt at a Solution I simply used the equation given above, but instead of getting 2Re{...} I...

not all functions are wavefunctions. For functions to be wavefunctions they have to obey a series of "rules". Now, my question is: there are many functions, which obey these rules which aren't eigenfunctions of the hamiltonian, thereby meaning that they don't obey the Schrodinger Equation...

What's the difference in the representation of spherical harmonics and the orbitals themselves? they look exactly the same to me... unlike the radial part of the wavefunction though.

Homework Statement psiplus = 1/sqrt(2) (psi(1,2) + psi(2,1)) Is PsiPlus an eigenfunction of the Hamiltonian operator? If so, what are the eigenvalues for the energy corresponding to PsiPlus in units of (h^2/(8ma)^2)? Homework Equations psiplus = 1/sqrt(2) (psi(1,2) + psi(2,1)) psi12...

...that's the title of a recent communication in the Journal of Chemical Physics[1] (as communication it is free access to everyone): http://jcp.aip.org/resource/1/jcpsa6/v136/i3/p031102_s1 The authors perform some rather clever looking algebraic transformations and arrive at a...

Homework Statement The wavefunction for a particle in one dimension is given by ψ1. Another state the particle may be in is ψ2. A third state the particle could be in is ψ3. Looking at the wavefunctions, ψ3 is ψ1 and ψ2 added together. Is the probability of being in a given interval in...

Hello forum, I'm new here. Please bear in mind I'm not a physicist, I'm sure you hear this a lot but anyway. I've recently taken an interest into quantum chemistry. So my question is the following: I understand electronic and nucleic wave functions are complex. When they are multiplied by...

Sorry if this question has been asked a million times. Either way, I'm working my way through Griffiths. It's a fantastic book--he doesn't try to slip anything past the reader. He is completely honest, and he doesn't abuse mathematics the way most authors do (screwing around with the Dirac...

I have a very poor understanding of how an electron "actually exists" in a crystal -- how it can be visualized. So conduction band electrons are supposed to be plane waves modulated by a periodic wavefunction (my understanding of Bloch theorem). This means they're basically everywhere in the...

Quantum Gravity is the successful merging of the two.. Wave functions (or QM) and Spacetime. So it would be good to know how the two differs. They seem to have one thing in common.. they are both mathematical abstraction. But then someone said (Peterdonis): "Tidal gravity is not "just a math...

Given 2 wavefunctions with respect to (r,theta,phi)... To prove that the functions are orthonormal, you would let the first w.function = Y(psi) and the 2nd = Y* (psi star), then you would integrate --> SY*Y dr dtheta dphi (integral of psi* times psi) dr dtheta dphi. Correct?

Homework Statement The position and momentum wavefunctions are Fourier transform pairs. If a particle has a perfectly defined position wavefunction Psi(x) = delta(x - x0), then what is its momentum wavefunction? Is this function normalizable? Homework Equations Fourier transform...

1. PROBLEM Q: write down an expression for a superposition wavefunction \Psi(x) for an electron in a 1D box of length L consisting of the n = 1, 2, and 3 states. show that C12 + C22 + C32 = 1, and Cn represents the coefficients of the n state. 2. RELEVANT EQUATIONS see word document...

Why do we associate the energy eigenstates with the "wavefunction" and "position"? This is something that has bothered me for a long time but that I never got around to asking. I suspect I'll feel like an idiot for not knowing this but anyway... One of the first things I was introduced to...

Homework Statement I'm investigating the Hylleraas method for helium using the basis states given below. I'm attempting to plot single particle wavefunctions and so want to integrate this basis function over all space for one of the particles, that is I want to calculate...

hey, i am concerned with landau levels and wanted to ask you whether you have a link, where one can see the orbitals- just like the orbitals for the hydrogen atom- for at least a few electron states? otherwise it would be sufficient if you could give me a hint how to calculate them. i...

I have two wavefunctions that I need to normalize but I cannot figure out how to get them into an acceptable integrable form... the first is psi=(2-(r/asub0))*e^(-r/asub0) the second is psi=rsin(theta)*cos(phi)*e^(-r/2asub0) I know these need to be in the form (where psi will be name y for...

Dear users, I am dealing with the proof of the Hellman Feynman-theorem for time-dependent wavefunctions given by the Wikipedia: (http://en.wikipedia.org/wiki/Hellmann%E2%80%93Feynman_theorem#Proof_2) I got stack: \begin{align} &\frac{\partial}{\partial...

Hello I have a question if someone could help I would be grateful. We have a wave function \psi(r,\theta,\varphi) = R_{5,4}Y_{l,m} + R_{5,3}Y_{3,0} + R_{5,2}Y_{2,1} which is describing a hydrogen atom. I have to find out for what values of the orbital quantum number and magnetic quantum...