Wave functions Definition and 148 Threads

Let me preface this by saying I am no physicist. This is a hobby of mine, and I'm trying to piece together knowledge as pick it up from different sources. I understand the particle/wave duality of particles like electrons (at least I think so). I cannot grasp, however, the leap in thinking...

Homework Statement To determine whether two wave functions, \psi_{1} and \psi_{1} correspond to the same quantum state of a particle. Homework Equations Calculations (simplified): \psi_{1}(x,y,z)=A \psi_{2}(x,y,z)=e^{z}A The Attempt at a Solution The two wave functions do...

If 2 particles have wave functions w1 and w2, in which W = w1 + w2 is a superposition of the wave functions, then would the probability density of W correspond to the probability of finding both particles at the same position within some interval of space?

The Hermite Polynomials are solutions to the Schrödinger equation for the Quantum Simple Harmonic Oscillator. But the Hermite Polynomials are real, not complex. I thought that solutions to the Schrödinger equation always had to be complex. What am I not understanding? Thanks in advance.

I've just finished my first year on a Physics degree course at uni, and I'm a bit confused about some of the concepts we've covered. I was hoping someone could straighten things out for me. We were told about wave-particle duality and de Broglie and how he came up with the idea about...

Hi, I asked this question in the quantum physics forum https://www.physicsforums.com/showthread.php?t=406171 but (afaics) we could not figure out a proof. Let me start with a description of the problem in quantum mechanical terms and then try to translate it into a more rigorous mathematical...

Hi, I discussed this with some friends but we could not figure out a proof. Usually when considering bound states of the Schrödinger equation of a given potential V(x) one assumes that the wave function converges to zero for large x. One could argue that this is due to the requirement...

It is sometimes said that wave functions are not real, and simply represent the observer's knowledge of the system. I would like to comment against this point by presenting an experimental setup which would tend to indicate that the wave function is quite real. As far as I know, this setup per...

May anyone help me with these questions 1 why is a dipole neutral as it completely resembles a system of two charges 2 i know probably its very advanced, but can anyone give me out a scope on wave function and its relation to energy of an orbital 3 am not sure if this is the right forum...

We know that Helium can have basically the same solution as the Hydrogen atom if there is only one electron. You get the same equation with a different factor on the potential and the basic solution is the same as the Hydrogen atom. But I'm trying to figure out why it can't work the other way...

Hi, i need some help regarding normalization of a wave function, i feel it is a very simple problem, but i am having a hard time figuring it out. I would really appreciate it if anybody could help me out a bit regarding this. I need to normalize the following wavefunctions by figuring out the...

friends,now, this may sound strange , but still... in my text while solving one dimension problems like barriers, step potential etc i noticed that they use a free particle eigenfunction coming from left ,. now why that is so did? i mean , if i need to describe a moving particle , will i...

Homework Statement A particle of unit mass moving in an infinite square well, V=0 for |x|<= a , V=∞ for |x|>a , is described by a wave function u(x) = Asin(3πx/a). (i) If I normalise the wave function, what is A? (ii) And what is the energy of state described by this wave function...

Homework Statement Consider the wave packet \psi\left(x\right)=\Psi\left(x,t=0\right) given by \psi=Ce^{\frac{ip_{0}x}{h}-\frac{\left|x\right|}{2\Delta x} where C is a normalization constant: (a) Normalize \psi\left(x\right) to unity (b) Obtain the corresponding momentum space wave...

So far I have learned these (correct me If I am wrong) A photon can be considered both an wave and particle. The wave equivalent of the photon is the superposition of Electric and Magnetic Field Waves. Similarly, De Broglie expanded this concept into matter. He proposed that Every matter has...

what are wave functions

We know, a particle may be represented by a wave PACKET which has a group velocity. But most of the time, we are concerned with the wave FUNCTION of a moving particle. In the de broglie hypothesis, it is said that a wave equation y=e^i(kx-wt), CANNOT be associated with a moving particle as the...

Homework Statement Consider the wave packet defined by psi(x) = integral(limits of +infinity and - infinity) dke^(-alpha(k-k_0)^2) e^(ikx) a)What is the mean value of the momentum p barred (it's just a line over the p) of the particle in the quantum state given by this wave function...

Homework Statement http://img200.imageshack.us/img200/9268/29360438.jpg Homework Equations P=\left|\Psi \right| ^{2}dV The Attempt at a Solution Okay, so r^{2} = x^{2}+y^{2}+z^{2} and \left|\Psi \right| ^{2} = A^{2}e^{-2\alpha r^{2}} . The volume of the of the bit we're...

Hello, In my QM class last semester, I produced a proof that wave functions must be continuous (used for boundary conditions, etc.) It was an undergraduate level course, so I don't know how easy it would be to do if you had more in the way of theory... But I've been wondering lately...

Homework Statement I have a series of functions, states, and levels that I'm suppose to graph using excel. Only problem is I'm not even sure of what to do. I'm completely confused/lost. Homework Equations n=1 l=0 R(r)=\frac{2}{a_0^{3/2}}e^{-r/a_0} n=2 l=0...

I am a filmmaker, and I have some questions about wave functions. I have read as much in English as possible (as opposed to math language) but unfortunately, I haven't dedicated my life to mathematics and understand math languages, so I suppose I'm asking for an explanation in English. I had...

Can anyone explain why these two field patterns are so similar? The (3,2,1) hydrogen wave function, and this pattern generated from a magnet on a CRT. (attached to post)

Homework Statement Show that a wave function is phase-shifted by (pi)/2 when multiplied by i and by (pi) when multiplied by −1. Homework Equations The wave function form I am using is function = A(cos(kx-wt)+isin(kx-wt)) But it was not specified which kind I can use The Attempt at a Solution...

Understanding the construction of vector spherical wave functions! Hi guys, I'm looking at electromagnetic scattering just now, and in particular, how multipole fields are constructed and then how the wavefunctions are represented as the incident, internal and scattered fields. When you...

Why are wave functions, e.g., Schrodinger's, based on the complex exponential function (e^{}ix) and not trigonometric functions (sine or cosine)? See Euler's formula for their relationship: http://en.wikipedia.org/wiki/Euler%27s_formula Furthermore, by using the complex exponential...

Hello all. I’m researching rotational motion with a nearly harmonic potential using the basis of the particle on a ring eigenstates e(n*i*theta) defined from theta=0 to theta=2*pi. The total systems wave functions (eigenfunctions of the full Hamiltonian (KE+PE)) are then linear combinations of...

Homework Statement I've had lectures on the theory of this topic, but I've not been given any examples and I'm struggling with how to apply the theory to this homework question: A particle is described by the normalised wave function Si(x,y,z)=Ae^-h(x^2+y^2+z^2) where A and h are real...

[SOLVED] Normalization of wave functions Mainly my question is that with the normalization of a wave function in quantum mechanics we use \int_\infty^\infty |\Psi(x,t)|^2 dx = 1 and we can solve for a constant we may have been given in the problem. Homework Statement Determine...

Homework Statement http://aycu20.webshots.com/image/43659/2005653976182996826_rs.jpg Homework Equations The Attempt at a Solution please can someone point me in the right direction - i have read the textbooks, looked at the lecture notes and i don't have a clue what to do.

[SOLVED] wave functions I realize that I have to provide what I have done first for every problem, but this one has stumped be. It is a bonus problem provided by my teacher and it is beyond our scope. that's why its a bonus. Just helping me start it would be a big help. thank you...

I have one question about wave functions and molecular orbitals (MO). In the computational quantum chemistry scientists often use Linear Combination Atomic Orbitals (LCAO) to construct MO. \varphi_{i\lambda\alpha}(\vec{r})= \sum\limits_{p=1}^{N}\chi_{p\lambda\alpha}(\vec{r}) C_{i\lambda p}...

Homework Statement Determine the energy levels, their degeneracy and wave functions (in ket notation) of a particle with spin quantum number s =1 if the Hamiltonian is AS_x^2 + AS_y^2 + B S_z^2 where A and B are constants. The Attempt at a Solution' I've spent ages thinking about this...

[SOLVED] to check if these wave functions are normalized to 1 I need to check if the following radial functions are properly normalized to unit probability R(1,0) (r) = 2(1/ao)^3/2 e^(-r/ao) R(2,1) (r) = (1/2*ao)^3/2 *[ r/ sqrt(3)*a0] e^(-r/2ao) We...

I am taking a second course in Quantum Mechanics right now, and one thing is bugging me... The wave function gives us the probability distribution of a particle being in some position. But which part of particle is it talking about? The center of the particle? But then how can you give a wave...

Noether's theorem relates symmetries and conserved quantities, eg. if the Lagrangian is invariant under a spatial translation, you have have conservation of momentum. For continuous systems, the conserved quantities become conserved "currents". Anyone know what symmetry is associated with...

Hi all, why a wave function has to be a continuous function?

Homework Statement Show that the (1,0,0) and (2,0,0) wave functions listed in table 7.1 are properly normalized. http://www.geocities.com/greenlran/phtable712.jpg Homework Equations psi.n.l.ml.(r,theta,phi)=R.n.l.(r)THETA.l.ml.(theta)PHI.ml.(phi) The Attempt at a Solution To...

1-Why is the probability of finding a particle at specific position at a certain time proportional to |Ψ|2? 2- Waves are represented by sinusoidal or complex functions. Why did we choose a complex function to represent matter waves instead of sinusoidal?

I am not looking for any answers, just some guidance. Consider case (c), (case (c) involved two waves with equal wavelength and amplitude, but with some arbitrary phase difference), and write the two waves as y1(x) = Acos((\frac{2*\pi*x}{\lambda})) y2(x) = Acos((\frac{2*\pi*x}{\lambda}) +...

Microscopic matter particles have associated wave functions, so do photons. The (probability) wave functions of photons are the classical EM waves. But don’t have EM waves another reality than matter probability waves? Isn’t the wave/ particle dualism of another kind for EM-waves/ photons than...

Hi everyone, I've confused myself trying to understand Weyl spinors... here's my best attempt at well-posed questions: (by the way, a nice--if incomplete--reference on computations using Weyl spinors can be found http://www.courses.fas.harvard.edu/~phys253b/handouts/WeylFeynman.ps , from...

I'm trying to normalize the even wave functions for the finite square well. The wave function is: \psi(x)= \begin{cases} Fe^{\kappa x} & \text{for } x< a\\ D\cos(lx) & \text{for } -a\leq x \leq a\\ Fe^{-\kappa x} & \text{for } x> a \end{cases} How can I determine D and F? When I...

Ok here's the deal. The problem gives me this wave function: y= (15cm) cos[(pi/5cm)x - (pi/12s)t] I undserstand that 15cm represents the amplitude, 5cm represents the wavelength, and 12s represents the T. What I don't get is that the standard wave function is in this form: y(x,t)= A...

I'm new (obviously) to these forums, so please direct me if I am in err. Just a quick question: A wavefuntion is the function that determines the location of a particle (the probability) right? And what is a non-linear wavefunction?

help, i can't figure out the question. All i know is that these wave functions all can have physical significance; which baffles me since the question is not likely. any ideas? http://img.photobucket.com/albums/v135/mykel_dg/help.jpg PICTURE OF THE PROBLEM and WAVE FUNCTION

Is there a version/subfield of QT that models the interactions between different wavefunctions? Something like Newtonian mechanics, but on the wavefunction level. E.g. you have two wave functions of (x,y,z,t), and you use the functions to find when and how they would affect each other and what...

Does it matter if we use one wave function to describe both electrons of a helium atom, or we need to use one wave function for each? Is there any empirical evidence of the right way?