Wave function Definition and 865 Threads

For the harmonic oscillator, I'm trying to study qualitative plots of the wave function from the one-dimensional time independent schrodinger equation: \frac{d^2 \psi(x)}{dx^2} = [V(x) - E] \psi(x) If you look at the attached image, you'll find a plot of the first energy eigenfunction for...

Homework Statement Show that the displacement D(x,t) = ln(ax+bt), where a and b are constants, is a solution to the wave function. Homework Equations I'm not sure which one to use: D(x,t) = Asin(kx+ωt+φ) ∂2D/∂t2 = v2⋅∂2D/∂x2 The Attempt at a Solution I'm completely lost on where to start...

Why is it that bosons (particles having symmetric wave functions) have integral spins and fermions (particles having antisymmetric wave functions) have half integral spins? A lot of books state this without specifying the reason. I was wondering if this is a theoretical deduction. Or is it an...

Greg Bernhardt submitted a new PF Insights post Interview with Astrophysicist: Adam Becker Continue reading the Original PF Insights Post.

I am continuing to work through Lessons on Particle Physics. The link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf I am on page 22, equation (1.5.58). The authors are deriving the Hermitian conjugate of the Dirac equation (in order to construct the current). I am able to...

Homework Statement I am being asked to show that the wave function ψ and dψ/dx are continuous at every point of discontinuity for a step potential. I am asked to make use of the Heaviside step function in my proof, and to prove this explicitly and in detail. Homework Equations...

Homework Statement Given the wave function Ψ(θ,φ,r)= f(r,θ)·[cosφ+cos2φ-i(senφ+sen2φ)] for an electron. (φ is the azimut) -Does it spin arround the z axis? -What kind of polarization has? It is dextrogyre or levoryre? -What are the posible values of Lz and what are they respective...

Homework Statement Show that the normalized wave function for a particle in a three-dimensional box with sides of length a, b, and c is: Ψ(x,y,z) = √(8/abc) * sin(nxπx/a)* sin(nyπy/b)* sin(nzπz/c). Homework Equations Condition for the normalization: ∫0adx ∫0bdy ∫0cdz Ψ*(x,y,z)Ψ(x,y,z) = 1...

Take a wavefunction ##\psi## and let this wavefunction be a solution of Schroedinger equation,such that: ##i \hbar \frac{\partial \psi}{\partial t}=H\psi## The complex conjugate of this wavefunction will satisfy the "wrong-sign Schrodinger equation" and not the schrodinger equation,such that ##i...

I read in Griffith's quantum mechanics that in a particular system, the second time measurement of the position (say) would yield the same result (the same collapse or the same spike)given that the measurement is done quickly (since it soon spreads out). I don't understand how quick this is...

Can the wave function in four dimensions be expressed as e^i(kx+ky+kz-wt)?

Homework Statement At ##t = 0##, a particle of mass m in the harmonic oscillator potential, ##V(x) = \frac1 2 mw^2x^2## has the wave function:$$\psi(x,0)=A(1-2\sqrt\frac{mw} {\hbar} x)^2e^{\frac{-mw}{2\hbar}x^2}$$ where A is a constant If we make a measurement of the energy, what possible...

Electron in hydrogen atom is defined by this wave function : Ψ(r,ϑ,φ)=Ar2exp(-2r/a)cos2(ϑ)exp(-3iφ) proton is in the center of the coordinate system.a is a known positive constant. I'm trying to find normalizing constant A. Ψ*(r,ϑ,φ)=Ar2exp(-2r/a)cos2(ϑ)exp(3iφ) I get that ∫∫∫(ψ*)ψdV=1...

Homework Statement Show that the (1,0,0) and (2,0,0) wave functions are properly normalized. We know that: Ψ(1,0,0) = (2/(a0^(3/2))*e^(-r/a0)*(1/sqrt(2))*(1/sqrt(2*pi)) where: R(r) = (2/(a0^(3/2))*e^(-r/a0) Θ(θ) = (1/sqrt(2)) Φ(φ) = (1/sqrt(2*pi)) Homework Equations (1) ∫|Ψ|^2 dx = 1 (2)...

The moon orbits Earth at a radius of 3.84E8 m. To do so as a classical particle, its wavelength should be small. But small relative to what? Being a rough measure of the region where it is confined, the orbit radius is certainly a relevant dimension against which to compare the wavelength...

In Born interpretation of the wave function it notes that the matter itself cannot be measured however the square of its absolute value is measurable. I am lost as to why the product can be measured but not the wave function itself. Can someone provide clarity?

We laymen and newbies are taught the Schrodinger equation was deterministic. So we tend to picture it’s like a classical thing.. some forever thinking it that way where the idea is etched deep in the mind. Yet when we are home with the idea it is deterministic (that is.. when not measured)...

1. “The profile of a transverse harmonic wave, traveling at 1.2 m s^-1 is given by y(x)=(0.02 m)sin[157 rad m^-1)x]. Determine amplitude, wavelength, frequency, angular frequency, and period. Homework Equations y(x,t)=Acos(kx-wt)[/B]The Attempt at a Solution I attempted to change it to a...

If two electrons are far apart, the antisymmetrization part in the probability amplitude for position is negligible and they behave as classical particles, thus we don't need to consider antisymmetrization. My question is why is this also true when we have a large number of electrons, say...

When solving problems, particularly in optics, it is often that we represent the wave-function as a complex number, and then take the real part of it to be the final solution, after we do our analysis. u(\vec{r},t)=Re\{U(\vec{r},t)\}=\frac{1}{2}\left(U+U^*\right) Here U is the complex form of...

I remember from my physics classes that the wave functions for the hydrogen atoms or an electron in a box showed typical linear wave behaviour. However, when you have a large system's wave function, say for example the universe, will it then show different spatial-dynamic structure? What comes...

In a dark energy dominated universe, it seems that all the particles get away from each other and that the final state will be one with one or zero particles per horizon. This sounds very intuitive, but it is based on classical physics and GR. Particles have wavefunctions and this is whar...

Why does a wave function collapse when we observe a particle? I would like to know why something that is in Super Position suddenly chooses a particular position when observed? If something is in all positions or states. How does the particle choose a particular state? What is the decision...

Homework Statement [/B] Ignore the suggested Problems if you will. If you can't see the image give me a shout and I'll give the problem statement here. Homework Equations B(y,t)=Bmaxcos(Ky-Wt) Wavelength=2pi/kn W=2pi*Frequency V=Emax/Bmax V=Walength*Frequency The Attempt at a Solution So...

Relative to the observer, objects shorten when approaching the speed of light exponentially. Does this rule also apply to the wave function? Does this rule also apply to massless particles like Photons? Or am I just simply forgetting something?

The classic limit of Schrodinger equation is hamilton-jacobi eqution. Wave function's classic limit is ##\exp{\frac{i}{\hbar}S(x,t)}##,##S(x,t)## is the action satisfying hamilton-jaccobi eqution. However, a particle travels along single trajectory of ##S(x,t)##, Why not make some constrains...

Hi, I'm recently reading something which briefly introduces C symmetry. So the thing that confuses me is that how does the spatial wave function contribute the (-1)^L factor? Thanks!

Homework Statement given: A wire loop with a circumference of L has a bead that moves freely around it. The momentum state function for the bead is ## \psi(x) = \sqrt{\frac{2}{L}} \sin \left (\frac{4\pi}{L}x \right ) ## find: The probability of finding the bead between ## \textstyle...

I am a beginner in quantum mechanics. I started out with D. J. Griffiths' book in quantum mechanics. I'm having a problem in understanding the wave function. What is the physical meaning of the wave function? I searched on the net but didn't get any good explanation. I understand that the...

If you know where to look for an electron (e.g. in an atom or an experimental setup) it is quite understandable that, until you know exactly where it is, there is a calculable probability of where it might be. However, if we take the case of an un-associated electron in space, it would seem that...

I'm well aware of the common adage and quantum fact that, until a particle is measured by some sort of instrument, it exists in a state of superposition, can interfere with itself, etc. My questions pertains to the definition of "measurement". In order for something to qualify as a measurement...

Hi! 1. Homework Statement From the website http://www1.uprh.edu/rbaretti/MomentumspaceIntegration8feb2010.htm we can see the Fourier transform of the ground state hydrogenic wave function : Φ(p) = ∫ ∫ ∫ exp(-i p r) (Z3/π )1/2 exp(-Zr) sin(θ) dθ dφ r² dr (1.1) After intregation...

Homework Statement In Griffiths' book "Introduction to Quantum Mechanics", Section 2.3, Chapter 2, the Fig. 2.7 gives the plots of the wave function (##\psi_{n}##) and its modulus of the harmonics oscillator, see the Appendix. With the order (##n##) increasing, they become both higher. However...

Homework Statement An electron coming from the left encounters/is trapped the following potential: -a<x<0; V=0 0<x<a; V=V0 infinity elsewhere the electron has energy V0 a)Write out the wave function b)normalize th wave function Homework EquationsThe Attempt at a Solution for -a<x<0...

Hi All, Perhaps I am missing something. Schrodinger equation is HPsi=EPsi, where H is hamiltonian = sum of kinetic energy operator and potential energy operator. Kinetic energy operator does not commute with potential energy operator, then how come they share the same wave function Psi? The...

It is required to be continuous in the following text: The book's reason why wave functions are continuous (for finite V) is as follows. But for infinite V, ##\frac{\partial P}{\partial t}=\infty-\infty=## undefined, and so the reason that wave functions must be continuous is invalid...

The radiation of an atom was interpreted by time-independent schrodinger equation:electron was transformed from high energy level state to lower and emit a photon.Could we treat this process through a wavefunction ##{\psi}(t)##? Before emiting,the system's wavefunction is ##{\psi}(0)## and after...

How come a+a- ψn = nψn ? This is eq. 2.65 of Griffith, Introduction to Quantum Mechanics, 2e. I followed the previous operation from the following analysis but I cannot get anywhere with this statement. Kindly help me with it. Thank you for your time.

In a recent article by BBM in Physical Review Letters highlights another approach to link QM to Zeta to Prove R.H. There approach proved unsuccessful. I want to ask professional Physicists if the following new approach have merit in connecting the Zeta function to QM? This new line of attack...

Homework Statement The wave function of a particle is known to have the form $$u(r,\theta,\phi)=AR(r)f(\theta)\cos(2\phi)$$ where ##f## is an unknown function of ##\theta##. What can be predicted about the results of measuring (a) the z-component of angular momentum; (b) the square of the...

Is there a function that describes the collapsing of a wave function? Or does in happen instantaneously in theoretical terms. I do want to know what happens with the other possible states, whether they stay alive but in another form, or what's going on.

The wave function for fermions has to be anti-symmetric with respect to exchange of positions of electrons, but what if it depends on wave vector as well. Does they have to be exchanged as well, in other words, for two-electron system what is correct Ψ(r1,k1,r2,k2) = - Ψ(r2,k1,r1,k2) or...

Lets assume there is an observable represented by the operator, ##\hat{A}##. It follow (I think) that the observed values and allowed states obeys an equation of the following form\begin{equation}\hat{A}|\psi^i\rangle=\lambda_f|\psi_f\rangle\end{equation} where $$|\psi^i\rangle = initial \ \...

In Shankars "Principle of Quantum Mechanics" in Chapter 4, page 122, he explains what the "Collapse of the State Vector" means. I get that upon measurement, the wave function can be written as a linear combination of the eigenvectors belonging to a operator which corresponds to the...

I don't understand "ψ (x,t) =Ae^i(px-Et)/h" I understand dψ^2/dx^2 = i^2p^2/h^2 but why dψ^2/dx^2 = -p^2/h^2 "-" from "i^2" missing please help me :frown::frown::frown::frown::frown::frown:

Let me start with a short disclaimer - I am not saying that QM is wrong or things like that. And I very well understand that my argument is not physical, more philosophical one, which may be considered as inappropriate here. Still, my intentions are good and I hope for some understanding. When...

Homework Statement I am having trouble with part d, where they ask me to prove that the wave function is already normalized The Attempt at a Solution But that clearly doesn't give me 1. I tried to use spherical coordinates since it is in 3D? Not really sure how to proceed. EDIT: I realize...

Homework Statement Show that the 3 wave functions are normalizedHomework Equations The Attempt at a Solution [/B] The above image is my initial attempt at the first equation. I was told the way to find out if its normalized is to use: ##\int^{+\infty}_{-\infty} \Psi^2 dx## = 1 but I...

Is there a possibility that none of the current interpretations of QM are right? Or is the current interpretations all that there will be on the table?

Homework Statement I'm a pharmacologist and I have a modern physics course to do. This is not my field and I'm completely lost... We were given this problem to do. Thanks a lot in advance. Consider a potential where U(x) = 0 for x ≤ 0 U(x) = -3E for x > 0 Consider a particle of energy E...