Hydrogen atom Definition and 397 Threads

There is an hydrogen atom on a electric field along ##z## ##E_z= E_{0z}## . Consider only the states for ##n=2##. Solving the Saecular matrix for find the correction to first order for the energy and the correction to zero order for the states, we have: ##| \Psi_{211} \rangle##, ##|...

In this case, ignoring derivatives that go to zero, (denoting the charge of the electron as q to avoid confusion) ##-\frac{\hbar^{2}}{2m} \frac{1}{r} \frac{\partial^{2}}{\partial r^{2}} (rAe^{-\frac{r}{r_{1}}}) - \frac{q^{2}}{4 \pi \epsilon_{0} r} Ae^{-\frac{r}{r_{1}}} = E A...

When studying the hydrogen atom, given that the potential depends only on the distance and not an any angle, we can do a separation of variables of the wavefunction as the product between a function depending only on the distance between particles (protons and electrons) and a spherical...

^^

I'm reading Carroll's GR book. I'm able to follow the introduction so far, but a couple of paragraphs are a bit hard to decipher: What exactly does "couples to" mean? Right now that's just a vague phrase to me that implies gravitational field has something to do with EM - but what's the...

I did this and I don't know if it's correct:

TL;DR Summary: Express through the Hubble constant the force that acts on the hydrogen atom due to the expansion of the universe We have a hydrogen atom, in a gravitationally bound system nothing interesting happens to it. Let's put it in an empty world with only an electron and a proton...

##\begin{align} \langle E \rangle &= \int_{\mathbb R^3} \int_{\mathbb R^3} \int_{\mathbb R^3} \int_{\mathbb R^3} g^\dagger (\tilde K) g(K) |\psi_0(x)|^2 \left(E_0 +\frac{\hbar^2 |K|^2}{2m}\right) e^{i(K-\tilde K)\cdot X -\frac{i}{\hbar} \left(\frac{\hbar^2 |K|^2}{2m}-\frac{\hbar^2...

I'm going to be a bit sketchy here, at least to start with. If you want me to show you exactly where I am I might post a pdf, if that's okay. (Only because it will simplify coding several pages of LaTeX.) Briefly, what I'm trying to do is take this system of equations: ##F^{ \prime } +...

The proton and electron are described by separate wavefunctions. When they come together in the hydrogen atom are they quantum entangled and have a joint wavefunction.

Hi, I asked this question elsewhere, but I didn't understand the answer. It seems to be easy to understand, but for some reason I'm really confuse. I'm not sure how to find the average position of an electron and the average separation of an electron and his proton in a hydrogen atom. To be...

Hello, I recently came across the following (apparent, I hope) paradox: suppose we have two H atoms. Now, a hydrogen atom is made up of one proton and one electron (fermions), so it is a boson. Then one could have two hydrogen atoms which are in the exact same state (including position). This...

Can you cite experiments where, in some excited states of a hydrogen atom, magnetic moment significantly differs from Bohr's magneton was detected? Correction for magnetic moment of nucleus is insignificant. Only experimental data, not theoretical forecasts. Starting from the experiments of...

my premises: — one can arrive at the Klein-Gordon equation by applying quantum mechanical operators to the special relativity dynamics equation E^2 = (mc^2)^2 + (pc)^2. — Schrodinger arrived at this equation, but rejected it because it didn't correctly explain the behavior of an electron in a...

Hi, I have an interview for masters degree program in 2 weeks and they asked to study two subjects thoroughly, first being Hydrogen atom and second being Kepler's laws. anyone recommends one book about each subject with advanced level questions that would help me understand the subjects to a...

I have a problem in calculate a matrix element in a problem with hydrogen atom. I have an hydrogen atom and Hamiltonian eigenstates ##|n,l,m>## where ##n## are energy quantum numbers, ##l## are ##L^2## quantum numbers and ##m## are ##L_z## quantum numbers, I have to calculate the matrix element...

I am a little lost on how to approach this problem. What I know is the following: The r vector is in terms of x y and z hat. I know my two l=0 states can be the 1s and 2s normalized wave function for Hydrogen. Should I be integrating over dxdydz?

Hello, I am trying to figure out the right way to approach this. First of all, other than the different Bohr radius value, does the change to a negative pion make any other difference to calculating the probability? Also what would be the correct way to apply the "small volume"? What I'm...

If you put a hydrogen atom in a box (##\psi=0## on the walls of the box), spherical symmetry will be broken so ##n##,##l##,##m_l## are no longer guaranteed to be good quantum numbers. In general, the new solutions will be a linear combination of all the ##|n,l,m_l\rangle## states. I know that...

I was reading in the Book: Introduction to Quantum Mechanics by David J. Griffiths. In chapter Time-independent Perturbation Theory, Section: Spin -Orbit Coupling. I understood that the spin–orbit coupling in Hydrogen atom arises from the interaction between the electron’s spin magnetic moment...

Hello! I went over a calculation of the hydrogen wavefunction using Dirac equation (this one) and I am a bit confused by the angular part. The final result for the wavefunction based on that derivation is this: $$ \begin{pmatrix} if(r) Y_{j l_A}^{m_j} \\ -g(r)...

While reading in the book of Introduction to Quantum Mechanics by David Griffith in the section of Fine structure of Hydrogen: spin- orbit coupling, he said that the average value of S operator is considered to be the projection of S onto J. I could not understand why he assumed that. please...

Hello everyone! I have two questions which had bothered me for quite some time. I am sorry if they are rather trivial. The first is about the general solution of the hydrogen atom schrödinger-equation: We learned in our quantum mechanics class that the general solution of every quantum system...

I read this from Nasa's website: "Within the first second after the Big Bang, the temperature had fallen considerably, but was still very hot - about 100 billion Kelvin (1011 K). At this temperature, protons, electrons and neutrons had formed, but they moved with too much energy to form atoms...

For spherical coordinate, ##dV = r^{2} \sin {\theta} dr d\theta d\phi## Therefore, $$<\frac{1}{r}> = \frac{1}{(\pi)(a_0)^{3}} \int_{0}^{\infty} {r e^{\frac{-2r}{a_0}} dr \int_0^{\pi} \sin {\theta}} d\theta \int_0^{2\pi} d\phi$$ From partial integral, I've found: $$\int_{0}^{\infty} r...

Hi, first-time poster here I'm a student at HS-level in DK, who has decided to write my annual large scale assignment on Schrödinger's equation. My teacher has only given us a brief introduction to the equation and has tasked us to solve it numerically with Euler's method for the hydrogen atom...

The equation $$\frac{\hbar^2}{2m}\frac{d^2u}{dr^2}-\frac{Ze^2}{r}u=Eu$$ gives the schrodinger equation for the spherically symmetric functions ##u=r\psi## for a hydrogen-like atom. In this equation, substitute an assumed solution of the form ##u(r)=(Ar+Br^2)e^{-br}## and hence find the values...

Reading the classical Feynman lectures, I encounter the formula(19.53) that gives the radial component of the wave function: $$ F_{n,l}(\rho)=\frac{e^{-\alpha\rho}}{\rho}\sum_{k=l+1}^n a_k \rho^k $$ that, for ##n=l+1## becomes $$ F_{n,l}=\frac{e^{-\rho/n}}{\rho}a_n\rho^n $$ To find ##a_n## I...

When we say energy levels of the hydrogen atom. Are that energies of the atom or of an electron in the atom? Also corresponding states? http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydwf.html Why energies are negative? E_n \propto \frac{-1}{n^2}

Hello,everyone. Can dynamical system be used to describe the behavior of the electron in Hydrogen atom?

This question is a followup to another thread. https://www.physicsforums.com/threads/qs-re-the-behavior-of-atoms-after-decoupling-completed.994581/ I would like to explore the issue raised by @kimbyd. . . . after reionization the temperature of the intergalactic medium is dominated by...

I am trying to solve the following exercise. In a H atom the electron is in the state described by the wave function in spherical coordinates: \psi (r, \theta, \phi) = e^{i \phi}e^{-(r/a)^2(1- \mu\ cos^2\ \theta)} With a and \mu positive real parameters. Tell what are the possible values...

First of all, I got to decide what I'm going to use to make the simulation. I know Fortran, Matlab etc but I'm pretty sure these won't help me much. I learned some C++ a couple years ago but my knowledge is rusty, however I think I'm going to use that combined with Unreal Engine, since it makes...

My textbook says "A is the area of the circle enclosed by the current" (produced by an electron in a hydrogen atom), A = ##\pi r^2 \sin(\theta)^2##. I don't understand where the ##\sin(\theta)^2## comes from.

I am unable to complete the first part of the question. After I plug in the function for psi into the differential equation I am stuck: $$\frac {d \psi (r)}{dr} = -\frac 1 a_0 \psi (r), \frac d{dr} \biggl(r^2 \frac {d\psi (r)}{dr} \biggr) = -\frac 1 {a_0}\frac d {dr} \bigl[r^2 \psi(r) \bigr] =...

I know how to solve this problem when the energy at ground state is zero but I don't know how to deal with 1st excited state energy as zero. According to me since the potential energy is zero therefore the kinetic energy must be 13.6eV according to conservation of energy. I also know that the...

I can not solve this problem: However, I have a similar problem with proper solution: Can you please guide me to solve my question? I am not being able to relate Y R (from first question) and U (from second question), and solve the question at the top above...

This is a general property of eigenvectors of Hermitian operators. State functions are a particular class of vector, and it is easiest to work in the general formalism (I am hoping to show how ket notation makes qm easier, not just do standard bookwork at this level). Suppose O is a Hermitian...

I am really stuck on what to do here in this question I have arrived at forming an equation to work out the radius of electron orbit from doing the following However I do not know what to do next as I don't know what the value of n (quantum number) must be? :oldconfused: Any help would be...

Why energy of the electron in ground state of hydrogen atom is negative ##E_1=-13,6 \rm{eV}##? I am confused because energy is sum of kinetic and potential energy. Kinetic energy is always positive. How do you know that potential energy is negative in this problem?

hi guys i am having a little problem concerning the theta part of TISE : its clearly that its very similer to the associated Legendre function : how iam going to change 1/sinθ ... to (1-x^2) in which x = cosθ i tried many identities but i am stuck here . any help on that ?

Is it possible to find a hydrogen atom which atomic nucleus is on Earth and electron is on moon?

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I’m not sure if this belongs in classic or quantum physics... but here it is...Is it possible to calculate the “voltage” between an electron and a proton in a ground state hydrogen atom?I know the ionization energy is 13.6 eV, so I assume it's safe to say the voltage is 13.6 volts at a certain...

Hello, I have a little problem understanding the quantum mechanics of a hydrogen atom. Im troubled with the following question: before i measure the state of a (simplified: without fine-, hyperfinestructure) hydrogen atom, which is the right probability density of finding the electron? is it...

Homework Statement Homework Equations VD= -1/(8m2c2) [pi,[pi,Vc(r)]] VC(r) = -Ze2/r Energy shift Δ = <nlm|VD|nlm> The Attempt at a Solution I can't figure out how to evaluate the expectation values that result from the Δ equation. When I do out the commutator, I get p2V-2pVp+Vp2. This...

Hi, I'm having trouble understanding angular moment of the one electron hydrogen atom. Solving Schrodinger equation on a referece system (say S) I get the energy eigenstates. They depend on three quantum numbers, n, l, m \frac{-ħ}{2 m}\nabla^{2} \Psi - \frac{e^{2}}{4 \pi \epsilon r} \Psi =...

Homework Statement Determined wave function in a hydrogen atom. ## Ψ(r,θ,Φ) = A(x+iy)e^{ \frac{-r}{2a_0}}## << find A by normalization Answer of a question in my book is ## A = -\frac{1}{a_0 \sqrt{8 \pi}} (\frac{1}{2a_0})^{3/2} ## Homework Equations ## \int Ψ^*(r,θ,Φ)Ψ(r,θ,Φ) d^3r = \int \int...

While separating variables in the Schrodinger Equation for hydrogen atom, why are we taking separation constant to be l(l+1) instead of just l^2 or -l^2, is it just to make the angular equation in the form of Associated Legendre Equation or is there a deeper meaning to it?