Wave mechanics Definition and 23 Threads

Suppose I have a perfectly circular pool which is four meters in radius, two meters in depth, and filled with water. Say I drop a steel ball with a radius of five centimeters into the middle of the pool from a height of five meters above the water's surface. After three seconds, what will be the...

I want to simulate 2D TM scattered fields (microwave range) for austria profile. Austria profile has 2 circles beside each other of certain dielectric and one ring below the circles. So basically I have three dielectric objects in the domain of interest and also positions of Tx and Rx are known...

Why are microphones pretty good at picking up sound that is much longer in wavelength than the size of the microphone? 1khz sound has a wavelength of around a third of a meter, varying a bit depending on atmospheric conditions. Yet a 1cm diameter electret microphone can pick it up reasonably...

Hello! So if I want to describe dΨ(x)/dt can I use 1D wave equation?

Homework Statement Do waves travel faster in dense or less dense mediums? As a wave moves from a less dense to a denser medium at a boundary end what properties change? (Wavelength, speed, frequency, amplitude...) If waves travel faster in solids then why do we hear better through air, and if...

Is it accurate to say that interference cannot happen in Statistical Mechanics? I know it is considered a wave mechanics phenomenon but aren't waves just highly statistical ensembles, like anything else? I always thought that Fourier says periodic spectra could be summed to create any signal...

Homework Statement a non uniform string of length L and mass M, has a variable linear density given by μ=kx where k is the distance measured from one side of the string and k is a costant. a) find that M=(kL2)/2 b) show that the time t required to a pulse generated from one side of the string...

Homework Statement Let ##\langle\psi| = \int^{\infty}_{-\infty}dx\langle\psi|x\rangle\langle x|.## How do I calculate ##\langle\psi|\psi\rangle?## Homework Equations ##\int^{\infty}_{-\infty}dxf(x)\delta(x-x_0)=f(x_0)## The Attempt at a Solution ##\langle\psi|\psi\rangle = \int\int...

"The Heisenberg picture does not distinguish time from space, so it is better for relativistic theories than the Schrödinger equation", says Wikipedia's entry on Matrix Mechanics. Since the Heisenberg equation of motion \frac {dA}{dt} = \frac {i}{\hbar} [H,A] + \frac {\partial...

If this seems like a homework question please forgive me, but it is merely for understanding and confidence building. I've been reading into the Bohr Model and the Wave Mechanics Model and I read through de Broglie and have proceeded to Schrodinger, Heisenberg and Dirac. At this stage, my mind...

What wave property changes as a bullwhip wave propagates toward the tip? Wavelength or amplitude? The problem seemed at first analogous to that of describing the behavior of a sound wave propagating through air of linearly decreasing density, except that sound is longitudinal.

Hi, When Heisenberg proposed the Matrix Mechanics. It was totally without the concept of waves. It didn't use de Broglie idea of matter waves. In fact, Heisenberg kept fighting about the wave concept. However, Matrix Mechanics is said to be equivalent to the Schroedinger Equation that uses...

I'm in a wave mechanics class and a homework assignment asks us to describe what would happen if a driving force is applied to m1, m2, or both. The explanation should be both calculational and written. I have no idea how to model this system in equation form! Help!

Homework Statement Two operators , A and B , satisfy the equations A=B^{\dagger}B+3 and A= BB^{\dagger}+1 a)Show that A is self adjoint b)Find the commutator of [B^{\dagger},B] c) Find the commutator of [B,B^{\dagger}] d) Suppose \varphi is an eigenfunction of A with eigenvalue a...

Homework Statement The operator Q satisfies the two equations Q^{\dagger}Q^{\dagger}=0 , QQ^{\dagger}+Q^{\dagger}Q=1 The hamiltonian for a system is H= \alpha*QQ^{\dagger}, Show that H is self-adjoint b) find an expression for H^2 , the square of H , in terms of H. c)Find the...

Homework Statement The operators P and Q are self-adjoint and satisfy the commutation relation [P,Q]=ic where c is a real number. Show that the operator [P,Q] is anti-self-adjoint, that is , that the adjoint of the operator is the negative of the operator, consistent with the right-hand side...

Hey there. I'm trying to redo basic quantum chemistry with a lot more rigor. I'm currently using Pauling's "Introduction to Quantum Mechanics With Applications to Chemistry". Here is a copy of the page(s) I will be referring to...

In this little Dover book "Wave mechanics", by Pauli, it appears to use h for hbar, and includes a footnote right on the very first page "1. In these lectures we use the symbol h to denote the quantity 1.05 x 10^-34 joule.sec. In the older literature this quantity was usually denoted by...

Wave Mechanics help--for optics course Homework Statement Consider a stretch string of length L along the x-axis in a stationary vibration mode of the form z(x, t) = z0sin((2*pi*n/L)x) cos(omega*t) where n is greater than or equal to 2 and is a given integer number and y0 and \omega...

Homework Statement 1. If Bohr’s theory and wave-mechanics predicts the same results for energies of hydrogen atom states, then why do we need wave mechanics with its greater complexity? 2. Compare Bohr’s theory and wave mechanics. In what respect do they differ? 3. Why don’t we observe...

Does it surprise you that the fundalmentals of wave mechanics fits so nicely into an inner product space. I assume this kind of algebra existed long ago but QM seem to fit perfectly into it. How amazing is that?

This is supposed to be an easy question, but I appear to be slightly lost. Can anyone give me a hint on what to do here? when waves of wavelength lambda are diffracted by a circular disc of diameter D the first minimum in the intensity of the scattered waves occurs at a scattering angle z...

Hi there, i need help in a couple of questions that I'm just stumped one of them : A) use induction to show that [ x (hat)^n, p(hat) sub "x" ] = i (hbar)n x(hat)^(n-1) - so far I've figured out this equation is in relation to solve the above eq, but I'm not entirely sure how to connect the...