Recent content by tomothy

1. Radial and angular distribution functions for an orbital Find the most probable value of theta and r for a 2pz orbital Homework Equations \psi _{2p_{z}} = N \textrm{cos}(\theta) r exp (-r/2) in units of a_0 The Attempt at a Solution Most probable r is when \textrm{d/d}r (P(r))=0...

Looks good. You may want to add why dU=0, because for an isothermal process, in general dU is not necessarily zero. It is true because dU, for a system which changes its volume by dV and temperature by dT, dU is also given by: \textrm{d}U=C_V \textrm{d}T + \left ( \frac{\partial U}{\partial...

This hamiltonian commutes with J^2 so it is separable into an angular part (the spherical harmonics) and an equation in r. The equation will only in general be solvable for j=0, if it is something like a harmonic potential or a morse potential. So the only way to get the rotational energy out is...

I'd like some help justifying the approximation that the vibrational and rotational motion of a diatomic molecule is separable. For two atoms of masses m1 and m2 the full hamiltonian is H=-\hbar ^2 /2m_1 \nabla _1 ^2 - \hbar^2 /2m_2 \nabla _2 ^2 + V(r-r_0) Where V(r-r0) is the potential...

I have a question about allowed transitions and molecular states. For an electric dipole transition between two states (say molecular or atomic) to have a non-zero probability of occurring, the transition dipole moment \langle \psi_{f}|\textbf{μ}\left|\psi_{i} \right \rangle must be non-zero...

I am trying to formulate a solution to the particle in a box energy eigenvalue problem, without solving a differential equation, instead using eigenvectors of p^2. My idea is to do this. Within the box (let's say it is defined between [-a,a] and within this region the hamiltonian is H={p^2}/{2m}...

What I really meant by the question was not what is meant by ψ oscillating. But rather what is ψ? I get that it's a complex function which varies, varying probability amplitude etc. But what I mean to ask is if ψ is a wave-like function, describing a particle, then what is vibrating? Like you...

Ah I think I get it. So no substance oscillates, but it's just a changing probability.

Obvious stupid question: what is a particle field?

'If particles also behave as waves, then what is oscillating?' I'm fairly sure that most people would consider this a nonsensical question. But I'm not sure why and I was hoping someone could clear this up for me. My thoughts are: The wave function is just a mathematical model, so don't...

I know this is more of a chemistry question but it's come to this I'm afraid. When calculating entropy changes in chemical reactions sometimes we students of chemistry use standard molar entropies of the reactants and products. But this surely doesn't account for the mixing effect. e.g. N2 +...

I think I've been using a textbook from about 18 years ago, so this could explain why. Thank you. (:

Just a quick question, I'm looking to express the normalisation condition formally mathematically, is this acceptable: 1=\int_R|\psi|^2 \ \mathrm{d}\tau For a particle in 3 dimensional region R.

My question is as follows. When (qualitatively at least) constructing molecular orbitals for a given molecule, a few "rules" are used to construct them. I'm wondering why the "rules" exist at all. For example, it is given that orbitals must have "similar energies" (however one quantifies...

I'm an A-level student (I don't know what the US equivalent is sorry, I'm not an undergraduate is what I'm saying), and I've independently done a project on wave functions for a few simple stationary systems; particle in a box and quantum harmonic oscillator are the ones I focused on in the end...