Wave functions Definition and 148 Threads

Hi, Short question: If you take the inner product of two arbitrary wave functions, and then the gradient of that, the result should be zero, right? (Since the product is just a complex number.) Am I missing something? ∇∫dΩψ_{1}*ψ_{2} = 0

Homework Statement I need to normalize the following wave function in order to determine the value of the coefficients. This is from the basic finite square well potential. \Psi(x) = Ae^{k_{1}x},for \ x < -a/2 \Psi(x) = Csin(k_{2}x),for \ -a/2 \leq x \leq a/2 \Psi(x) = De^{-k_{1}x}, for \ x...

Homework Statement A particle moving in one dimensions is in the state |\psi\rangle with position-space wave function \psi(x) = Ae^{−\lambda|x|} where A, λ are positive real constants. a)Normalize the wavefunction. b)Determine the expectation values of x and x^2 Homework Equations...

So consider a 2D system with a circular potential and a spin-orbit interaction: V(r) = V_0 \theta(r_0 - r) + c r_0 V_0 L_z S_z \delta(r-r_0) where θ is step function. So the operators Lz and Sz commute with the Hamiltonian are are therefore conserved quantities. For the same reasons...

Hello everybody Two questions concerning the notion of wave function. 1. Every quantum mechanics book describes the space of wave functions (or more generally of quantum states) of a given system as a Hilbert space. But correct me if I'm wrong QM also says that two elements of such a...

Homework Statement Consider the double Dirac delta function V(x) = -α(δ(x+a) + δ(x-a)). Using this potential, find the (normalized) wave functions, sketch them, and determine the # of bound states. Homework Equations Time-Independent Schrodinger's Equation: Eψ = (-h^2)/2m (∂^2/∂x^2)ψ +...

Note: I am completely self taught. I have only gone as far as Algebra and regular physics in high school. But I took the initiative to teach myself advanced physics and up to multivariable calculus from reading a book on the subject. So I may not be completely informed on everything present. I...

Hi, I'm a little confused about how to apply the real spherical harmonics when building a hydrogen wave function. I'm doing a computational project, so I want to work with a wave function which is strictly real, and I'm hoping I can do so by building the orbitals using the real spherical...

In my Physics I class, we started learning about wave functions in the form: y(x,t) = sin(kx ± ωt ± ∅) or y(x,t) = cos(kx ± ωt ± ∅) 1) I saw a question where the wave function was structured as: y(x,t) = sin(ωt - kx + ∅) and the answers for the direction of the wave was in the +x...

Hi, Can anyone explain to me why the wave functions in QM must to be complex, other than to make it work when inserted into the Schrodinger equation?

the wave functions of individual particles can be added together to create a wave function for for system, that means quantum theory allows physicists to examine many particles at once??...how is it possible if the wave function of each particles is different??...is it based on rules of...

This might sound like a totally dumb question but anyway: QCD lagrangian in the limit of mu=md has flavor SU(2) symmetry with respect these two quarks. And we say that these quarks' wave functions are eigenstates of I and Iz. The question is why? Thanks.

For multibosonic systems, as I understand, the wave function must always be symmetric (antisymmetric for fermionic, which this question easily generalizes to). But as far as I can see for N>2 you can easily construct a lot of other wave functions which are symmetric rather than the one my book...

Homework Statement Show that the following wave function eigenfunction decomposition is viable and find it's expected energy. ψ(x, t) = [1/(1+i)]ψ1(x)e^(-iw1t) - (1/√2)ψ2(x)e^(-iw2t) Homework Equations ∫ψ(x)*ψ(x)dx = 1 probability ∫ψm(x)*ψn(x)dx = 0 orthogonality ∫ψm(x)*ψn(x)dx...

My understanding of wave-functions is close to zero, pardon me if the questions don't sound proper. 1. Do we have wave-function usage to describe a) Coherence and b) Entanglement? 2. Has a (mathematical/conceptual) way been developed to show the complementarity between both (a & b) via...

what are electron and hole wave functions? how they overlap

Hello I have a problem in understanding wave functions Let q \mapsto \phi(q) a position wave function for a single particle of mass m The equivalent momentum wave function is said to be computable with using Fourier transform: \psi : p \mapsto \int_q \phi(q) \cdot e^{-i/\hbar \cdot \langle p...

1. Considering the helium atom, a. why do we use product type wave function b. how is the anti-symmetry taking care c what are the criterion for selecting best wave function d. how do we take into account the electron correlation Attempts: a. I think it is because we want exact wave...

here is a link to the pdf file with my question and answershttp://dl.dropbox.com/u/2399196/harmonic%20osc.pdf i'm not sure where to start, because i don't want to assume anything that i haven't been given. i'm stuck on part (iv) where i have to derive explicit expressions for 2 wave functions...

The empirical method of linear combination of atomic orbitals is not hard to understand. There is one thing about this method that doesn't make too much sense, though. Why are wave functions additive? This property of the wave functions is crucial for this method. Claiming that the wave...

Hi guys, I'm reading Shankar and he's talking about the Variational method for approximating wave functions and energy levels. At one point he's using the example V(x) = λx^4, which is obviously an even function. He says "because H is parity invariant, the states will occur with alternating...

Homework Statement Let ψ(r)= c_n ϕ_n (r) + c_m ϕ_m (r) where ϕ_n(r) and ϕ_m (r) are independent functions. Show that the condition that  is Hermitian leads to ∫ψ_m (r)^* Âψ_n (r)dr = ∫Â^* ψ_m (r)^* ψ_n (r)dr Homework Equations ∫ψ(r)^*  ψ(r)dr = ∫Â^* ψ(r)^* ψ(r)dr The Attempt...

With the number i, its possible to create a wave function with just one variable. example: f(x)=i^x or.. f(x)=2^ix But is there any wave function without the number i AND with only one(x and y) variable? can this be created?

In quantum mechanics, most wave functions are normalized with \int |\phi|^2 dx^3 =1. But I did not see any field in the quantum field theory is normalized. I understand they maybe just plain waves and does not need to be normalized. But in some cases, if we do not expand the field as plain wave...

OK, so i understand that wave functions have something to do with something...i'm clueless, please help on this one. First, what ARE wave functions? i haven't an answer that i can understand, explain this to me dumbed down please. Second, what do they do exactly in the double slit...

So I'm a little confused on the notation when working with wave functions constructed as a linear combination of an orthornormal basis set. Like on the form: \Phi=Ʃn cnψn If I want to find the expectation value represented by the operator O for the state described by \Phi, I would...

Is it true that the wave function of a particle is a probability wave related to its position?( probability wave for lack of a better terming/understanding) And if it does give any form of insight on its position, could this be related to the uncertainty principle in any way? Meaning could...

Hi, I'm looking through my teacher's notes and he says that a wave function for a sinusoidal wave can be written: y = A sin (ω t – k x) or y = A sin (k x - ω t) The textbook gives it in the second form. I think that using one over the other gives the same answer but in the opposite sign. I...

Suppose in one dimension we have a particle in box with the length a. If we were to expand it's ground state wave function in terms of the state functions of the particle in another box (with the length for example 10a), is the expand automatically zero in the region x>|a|?

I am currently reading through Griffiths Quantum Mechanics textbook, and on page 14, Griffiths proves that \frac{d}{dt}\int_{-\infty}^{\infty} |\Psi(x,t)|^2 \, dx = \left.\frac{i \hbar}{2m}\left( \Psi^* \frac{\partial \Psi}{\partial x} - \frac{\partial \Psi^*}{\partial x} \Psi \right)...

Hi, it says on Wikipedia here that "a particle in state n, and a particle in state m" is described by |n>|m>±|m>|n> rather than the naive |n>|m>. I can see why this is sensible on many accounts (eg, you'd want to preserve the predicted probability of finding blah under switching the...

consider a particle in one dimention. there is a dirac delta potential such as V=-a delat(x) the wave functions in two sides(left and right) are Aexp(kx) and Aexp(-kx) respectively. so the differential of the wave functions are not continious at x=0. what is the justification here?

Are wave functions and quantum waves synonyms? If not, how do the meanings differ? I'm asking because wave functions are mathematical abstractions and can't be real. But in Objective collapse theories, Bohmian mechanics, they are said to be real. Or more accurately, should the correct words...

Pretty basic question here, but I was wondering if someone could explain to me how to normalize a wave function. Specifically: ψn(x) = A * √x * sin (n∏x2/L2), n = 1, 2, 3, ... Normalized in the range 0 to L. Thanks for the help, a little bit of a walk through would be much appreciated.

Homework Statement Consider a potential well with infinite high walls, i.e. V(x)=0 for -L/2\leq x \leq +L/2 and V(x)=\infty at any other x. Consider this problem (the first task was to solve the stationary Schroedinger equation, to get the Energies and Wave Functions, especially for n=1 and...

Suppose I have a wavefunction ψ(r1, r2)= (∅1s(r1) ∅1p(r2) - ∅1s(r2) ∅1p(r1)) And I know that ∅1s(r1) and ∅1p(r1) are normalized. How would I go about finding the normalization constant for ψ(r1, r2)? Everywhere I look just whips out a \frac{1}{\sqrt{2}} out of nowhere...

1. Will wave functions collapse in a photon double-slit experiment after we place a detector at one of its slits and detect one photon? 2. Will wave functions collapse in a photon double-slit experiment after we detect a photon on the screen? 3. Will wave functions collapse in an electron...

If I draw a displacement-distance graph and a displacement-time for two wave forms, will both graphs look the same? With the exception of the x-axis label.

The situation I have in my problem is the standard infinite square well from 0 to L. The normalized eigenfunction is \phin(x) = \sqrt{2/L}sin(n\pix/L) for n=1,2,3,... if my wave function at time t=0 is then cos(a)\phi1(x)+sin(a)\phi2(x) is my wave function at more general time t something...

http://en.wikipedia.org/wiki/Quantum_entanglement#cite_note-0" Is there an experiment where bucky balls are entangled? Many of us have heard about bucky balls showing single particle interference in a double slit experiment. However I have not heard of them being entangled. I read the...

Homework Statement The displacement from equilibrium caused by a wave on a string is given by y(x, t) = (−0.00217 m)sin[(44.4 m−1)x − (728 s−1)t]. i need to find (b) number of waves in 1 m waves (c) number of complete cycles in 1 s cycles (d) wavelength (e)...

Biochemistry doesn't use the concept of wave functions because biochemistry deal with big things that are much larger than the quantum realm. But isn't it that stochastic quantum process can affect the probability of certain occurences that can amplitude up and affect Biochemistry? Chaos and...

I am reading over some quantum mechanics and have came across wave functions and probability densities. Needless to say I am Havin difficulties understanding exactly what they are. If anyone can help me understand what exactly they are and just any information please post it. Thanks

In various quantum chemistry books and course booklets I came across spin wave functions (usually referred to as alpha and beta for spin and up and down, respectively) that depend on a so called spin-variable. They are usually used to construct slater determinants. An example of this is Modern...

Hi guys, I have a question regarding electron wave functions. If an electron's wave function describes the probability of it being at a specific position, how can two wave functions destructively interfere (as occurs in the formation of anti-bonding atomic orbitals)? I can understand how the...

Homework Statement I have a quantum harmonic oscillator with quantum numbers nx,ny,nz ≥ 0 and frequency ω0. There are three parts to the problem. To me it seems they are out of order, but I'm kind of shaky deriving these. a) Write down the energy level Enx,ny,nz of a QHO in 3d with quantum...

Homework Statement So to test the variational method of simple harmonic oscillator I am using some functions that can be a good approximations, such as: Gaussian: \psi(x)=Ae^{-bx^2} Polynomial: \psi(x)=1-bx^2+\frac{b^2 x^4}{2} (I just expanded the Gaussian into Taylor, I can use just...

This is more of a calculator issue than the physics part. Below is just an example from my textbook. Our professor expects us to be able to plug an integral like this into our calculator to get the answer. although every problem I have tried like this just pops out another integral on the...

Homework Statement The problem, along with a solution, is attached as an image file. Homework Equations The Attempt at a Solution I have done the problem which was very straight forward. One simply had to look up the Rn,l and then plug in the appropriate quantum numbers. Since for...

What is the maximum size scale (how many atoms) where the concept of wave function is still useful in chemistry esp. biochemistry? For example. Wave function modelling is easily done in Hydrogen Atom. The interaction Hamiltonian is mostly of the nature E = K + P (Total Energy = Kinetic +...