3
votes
1answer
68 views

Spin-orbit coupling from the rest frame of the proton?

When we calculate the spin-orbit interaction in a Hydrogen atom we just work in the electron's frame of reference: the proton is moving and produces a magnetic field which the electron's spin ...
1
vote
2answers
85 views

Calculating the most probable radius for an electron of a hydrogen atom in the ground state

This link describes a method for determining the most probable radius of an electron for a Hydrogen atom in the ground state. It states that : The radial probability density for the hydrogen ...
10
votes
5answers
1k views

How does the hydrogen atom know which frequencies it can emit photons at?

At university, I was shown the Schrodinger Equation, and how to solve it, including in the $1/r$ potential, modelling the hydrogen atom. And it was then asserted that the differences between the ...
0
votes
1answer
42 views

Can scientists tell the energy levels of the atom?

In the hydrogen spectral series how did the scientists know the number of the energy level which the electron is moving from or to?
2
votes
0answers
41 views

Limits of integration for the radial wave function of the Hydrogen atom in the WKB approximation

I am working a problem where we have to find the energy eigenvalues for the radial wave function of the hydrogen atom for $\ell=0$ using the WKB approximation. I am sure that I set up the integral ...
0
votes
0answers
69 views

Difference between expectation values of $L^2$, $L_z$ and measuring $L^2$, $L_z$

I was given with this hydrogen radial wavefunction $$ R_{21} =\left(\sqrt{\frac{1}{3}}Y^0_1 + \sqrt{\frac{2}{3}}Y^1_1\right) $$ and was asked to find a) What are the expectation values of the ...
0
votes
1answer
73 views

Expectation value of energy from the position state of hydrogen atom [closed]

I was given with the position state of hydrogen atom: $$ R_{21} =\left(\sqrt{\frac{1}{3}}Y^0_1 + \sqrt{\frac{2}{3}}Y^1_1\right) $$ I am getting confused about getting the expectation value of ...
3
votes
2answers
215 views

What is the expected distance of the electron from the nucleus in the hydrogen atom?

Specifically, I would like to know the general formula, in terms of $n$ and $l$, assuming the electron is in an orbital (i.e. simultaneous eigenstate of $H$, $L^2$, and $L_z$). I understand that it ...
1
vote
1answer
58 views

Hydrogen atom: potential well and orbit radii

I happened to open up an old solid-state electronics book by Sah, and in it he says: "it is evident that the electron orbit radius is half the well radius at the energy level En" The orbit radius is ...
0
votes
0answers
60 views

Perturbation of a Hydrogen Atom in a Quadrupole Field

Question: A hydrogen atom is located in a quadrupole field, which gives it a perturbation $$H_1=A(x^2-y^2)$$ where $A$ is some constant. Calculate the ...
0
votes
3answers
167 views

Is any time-dependent hydrogen atom Schrödinger equation solvable analytically?

It's well-known that hydrogen atom described by time-independent Schrödinger equation (neglecting any relativistic effects) is completely solvable analytically. But are any initial value problems for ...
0
votes
1answer
69 views

Angular momentum of hydrogen from $n,l,m$ values

Given a wavefunction for hydrogen $\psi(n,l,m)$ it is possible to calculate its associated energy from $E=-13.6/n^2$. Does a similar equation exist for $L^2$ and $L_z$? That is, if we are given the ...
4
votes
3answers
612 views

Why is a proton assumed to be always at the center while applying the Schrödinger equation?

Why is a proton assumed to be always at the center while applying the Schrödinger equation? Isn't it a quantum particle?
6
votes
2answers
277 views

How can one see that the Hydrogen atom has $SO(4)$ symmetry?

For solving hydrogen atom energy level by $SO(4)$ symmetry, where does the symmetry come from? How can one see it directly from the Hamiltonian?
4
votes
2answers
364 views

What made Bohr quantise angular momentum and not some other quantity?

Bohr's second postulate in Bohr model of hydrogen atom deals with quantisation of angular momentum.But, I was wondering why he quantised angular momentum and any other quantity?
2
votes
1answer
108 views

Possible Outcomes from Measuring a Hydrogen Atom

A hydrogen atom is characterized by the wavefunction $$\mid \psi \rangle =\sqrt{\frac{2}{7}}\mid 4\,2\,1\rangle +\sqrt{\frac{1}{7}}\mid 2 \,1\,\bar{1}\rangle+\sqrt{\frac{4}{7}}\mid 3\,2\,0\rangle$$ ...
5
votes
1answer
259 views

Orthonormality of Radial Wave Function

Is the radial component $R_{n\ell}$ of the hydrogen wavefunction orthonormal? Doing out one of the integrals, I find that $$\int_0^{\infty} R_{10}R_{21}~r^2dr ~\neq~0$$ However, the link below says ...
1
vote
1answer
330 views

Writing a Wavefunction as a Linear Combination of Eigenstates

We have the following wavefunction for the hydrogen atom: $$\psi(r,\theta,\phi)=\frac{1}{\sqrt{4\pi}}\frac{1}{(2a)^{3/2}}\frac{r}{a}e^{-r/2a}\sin(\theta)\sin(\phi)$$ where $a$ is the Bohr radius. ...
0
votes
0answers
202 views

Orthonormality of Radial Wave Function in the Hydrogen Atom

Question: Show that the radial wave function for the hydrogen atom are orthogonal with no exceptions. Attempt: We know that ...
4
votes
1answer
500 views

Reduced mass in quantum physics (Hydrogen Atom)

I've gone through an intermediate classical mechanics course, and in solving the two-body problem, we reduce it to a one-body between a larger stationary mass, and a smaller reduced mass. Most ...
2
votes
1answer
77 views

Why does bringing N 1-orbital atoms together yield N levels?

A common example of this is that when bringing N hydrogen atoms together into a ring. Far apart, assume each electron exists in the 1s state. As we bring them together, instead of each electron ...
2
votes
1answer
107 views

Volume charge density of H-atom

I have a problem where I am supposed to calculate the volume charge density of a neutral hydrogen atom. The potential is given to be $$ \Phi = k \frac{e^{-ar}}{r} \left(1 + \frac{ar}{2}\right) $$ Now ...
1
vote
1answer
287 views

Hydrogen ground state energy calculation?

We want to find the energy of a hydrogen atom ($Z=1$) in the ground state $$ \psi_{100} = \frac{1}{\sqrt{\pi}}e^{-r}\ \ \ \ \ \ (\mbox{atomic units}) $$ with Hamiltonian $$ H = ...
0
votes
0answers
31 views

How to calculate the binding energy of electron of hydrogen atom by using uncertainty principle? [duplicate]

How to calculate the binding energy of an electron of hydrogen atom using uncertainty principle?
1
vote
2answers
130 views

Transition integral from 1-D cartesian into 3-D polar coordinate system

Lets say we have an electron which can be in two states. Its wavefunction for two states is then $\Psi=A\Psi_n + B\Psi_m$, where $\Psi$ is time dependent wave function. I know that the transition ...
1
vote
2answers
1k views

The probability of finding the electron in the H-atom

In the book Arthur Beiser - Concepts of modern physics [page 213] author separates the variables in the polar Schrödinger equation assuming: $$\psi_{nlm}=R(r)\Phi(\phi)\Theta(\theta)$$ then there a ...
2
votes
1answer
184 views

Orbital of Hydrogen molecule

does anybody here know an analytical approximation of the bonding hydrogen orbital MOLECULE? I am looking for a good approximation to this orbital, that might be in some textbooks to get an ...
0
votes
1answer
175 views

How to determine the region that would contain a quantum particle

(a) A hydrogen atom is in its ground state. If space is divided into identical infinitesimal cubes, in which cube is the electron most likely to be found? If instead space is divided into 31 ...
1
vote
1answer
480 views

Solution of 1-D Schrodinger equation for the potential $V(x) = -\frac{1}{|x|}$

May be this question might have already been asked but i couldn't find it, so let me know if its already there. Consider a potential, $V(x) = -\frac{1}{|x|}$ and if we apply this to a one dimensional ...
3
votes
1answer
224 views

How can we describe the electrons of multi-electron atoms (i.e. not Hydrogen) when equations/analytic solutions only exist for Hydrogen?

I've been digging into emission spectra of different elements and found that such things as the Rydberg equation, Bohr's model, and quantum mechanics can only fully describe the single electron in the ...
4
votes
1answer
870 views

Stark Effect on the 1st excited state of Hydrogen

I know the ground state of hydrogen is unaffected by the Stark effect to first order. And I also know that the 1st excited state is split from 4 degenerate states to 2 distinct, and 1 degenerate state ...
1
vote
1answer
330 views

Finding the wavelength of an electron in its ground state?

To find the wavelength of an electron in its ground state in a hydrogen atom, would I or could I do the following? Use the ground state energy (-13.6eV) in $E^2 = m^2c^4 + p^2c^2$ Solve for $p$ Use ...
2
votes
1answer
210 views

Ground state energy of hydrogen molecule ion

In this paper, it is mentioned: Furthermore, since the energy of $H_2^+$in the ground state must be lower than that of an H atom in the ground state,the negative (attractive) forces in the ...
2
votes
2answers
244 views

Why the hydrogen radial wave function is real?

Why the hydrogen radial wave function is real? Is it a coincidence?
3
votes
3answers
304 views

Bessel vs. modified Bessel in radial equation of hydrogen

I am trying to understand the difference between Bessel functions and modified Bessel functions (simply googling is yielding complicated, non-intuitive answers). I was under the impression that one ...
5
votes
2answers
333 views

Technical detail in the solution of the hydrogen atom

I'm trying to do an exercise in which you solve the Schrödinger equation for the hydrogen atom. Through the exercise, I've already shown that the wavefunction is: $$ \psi_{n\ell m}(r,\theta,\varphi) ...
2
votes
2answers
278 views

Hydrogen atom in quantum mechanics

I have problems following the calculations in Griffiths' Introduction to Quantum Mechanics (Chapter 4.2.1): If you apply the Schrödinger equation to the Coulomb potential you get the following ...
2
votes
2answers
242 views

What's the difference between two Hydrogen atoms?

If we are given two Hydrogen atoms, would the only difference between them would be their quantum state (Energy level or eigen value, and the corresponding Orbital or eigen state) and their location ...
4
votes
1answer
252 views

Scattering states of Hydrogen atom in non-relativistic perturbation theory

In doing second order time-independent perturbation theory in non-relativistic quantum mechanics one has to calculate the overlap between states $$E^{(2)}_n ~=~ \sum_{m \neq n}\frac{|\langle m | H' ...
1
vote
2answers
749 views

Wave function of Hydrogen Atom [closed]

Wavefunction of a Hydrogen atom is expressed in eigenfunctions as: $$\psi(\boldsymbol r,t=0)=1/\sqrt{14}(2\psi_{100}(\boldsymbol r)-3\psi_{200}(\boldsymbol r)+\psi_{322}(\boldsymbol r) ).$$ Is ...
1
vote
3answers
740 views

Expectation values of $(x,y,z)$ in the $|n\ell m\rangle$ state of hydrogen?

Expectation values of $(x,y,z)$ in the $| n\ell m\rangle$ state of hydrogen? Does anyone know of a quick way of finding this (if there is even one)? Can I somehow use the relation that: $$\langle ...
2
votes
1answer
455 views

Theoretical treatment of Hydrogen bond?

I would like to understand how the Hydrogen bond can be described through the Schroedinger equation. I don't need numerical methods that one uses them to simulate it, rather I need its treatment from ...
4
votes
2answers
806 views

magnetic moment of proton

I just tried to calculate the magnetic moment of a proton. I took the proton g-Factor of $g=5.585694$ nuclear magneton of $\mu_k = 5.050783 * 10^{−27}$ J/T proton spin of $I=1/2$ At first I ...
1
vote
1answer
73 views

Spectrum measurement

How can be spectrum of hydrogen measured (Lyman series, Balmer series, Paschen series and so on)? I mean schema of measurement circuit and the measuring technique (including all the steps needed). Is ...
4
votes
5answers
1k views

Hydrogen radial wave function infinity at r=0

When trying to solve the Schrödinger equation for hydrogen, one usually splits up the wave function into two parts: $\psi(r,\phi,\theta)= R(r)Y_{l,m}(\phi,\theta)$ I understand that the radial part ...
2
votes
1answer
218 views

Electric dipole transitions/expectation value of position

Part of a homework question asks to show that for $\ell=0$ in both $\Psi_i$ and $\Psi_f$, we have $$ \int \Psi_i^\ast \vec{r} \Psi_f \; d\tau = 0 $$ for the position vector $\vec{r}$. (This is for ...
2
votes
4answers
2k views

How can one describe electron motion around hydrogen atom?

I remember from introductory Quantum Mechanics, that hydrogen atom is one of those systems that we can solve without too much ( embarrassing ) approximations. After a number of postulates, QM ...
1
vote
0answers
431 views

Square of Laplace–Runge–Lenz vector in Hydrogen atom [closed]

I have a problem. I've tried this question, but I don't get the correct expression. Can someone give me some ideas? Thanks! Consider the Hydrogen Atom Hamiltonian: $$ H = (\mathbf p^2/2 ...
2
votes
1answer
569 views

Wave function of hydrogen atom including spin of nucleus

How do I write the wave function of hydrogen atom taking into consideration of nucleus spin? For example consider $2S_{\frac{1}{2}}$ state with nucleus spin $I$, then wave function ...
1
vote
3answers
278 views

Is energy conserved in decay of hydrogen atom in superposed state?

This looks like a paradox. Let's say we have an hydrogen atom. Superposition of states could be possible for electrons. But if an electron is in a superposition, I guess it could decay into a lower ...