In physics, the observer effect is the disturbance of an observed system by the act of observation. This is often the result of instruments that, by necessity, alter the state of what they measure in some manner. A common example is checking the pressure in an automobile tire; this is difficult to do without letting out some of the air, thus changing the pressure. Similarly, it is not possible to see any object without light hitting the object, and causing it to reflect that light. While the effects of observation are often negligible, the object still experiences a change. This effect can be...
Quantum tunnelling or tunneling (US) is the quantum mechanical phenomenon where a wavefunction can propagate through a potential barrier. The transmission through the barrier can be finite and depends exponentially on the barrier height and barrier width. The wavefunction does not disappear on one side and reappear on the other side. The wavefunction and its first derivative are continuous. In steady state the probability flux in the forward direction is spatially uniform. No particle or wave is lost.
Some authors also identify the mere penetration of the wavefunction into the barrier,...
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In this specific instance you are correct. If you have a hydrogen atom that is completely isolated from the environment, and which has been prepared in a pure quantum state given by a superposition of the $1s$ and $2p$ states, then yes, the charge density of the electron (defined as the electron ...
I came across this simple proof:
We show that Hermitian operators have real eigenvalues. The definition
of a Hermitian operator is
\begin{equation} \langle \phi_i | \hat A | \phi \rangle = \langle
\phi_i | \hat A | \phi \rangle^* \tag{1} \end{equation}
Then if $|\psi\rangle$ is a...In mathematics, particularly linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis). This is extremely useful because computations involving a diagonalizable matrix can often be reduced to much simpler computations involving the corresponding diagonal matrix. The concept of diagonalization is relatively straightforward for operators on finite-dimensional vector spaces but requires some modification for operators on infinite-dimensional spaces. In general, the spectral...
In electrodynamics, the Larmor formula is used to calculate the total power radiated by a non relativistic point charge as it accelerates. It was first derived by J. J. Larmor in 1897, in the context of the wave theory of light.
When any charged particle (such as an electron, a proton, or an ion) accelerates, it radiates away energy in the form of electromagnetic waves. For velocities that are small relative to the speed of light, the total power radiated is given by the Larmor formula:
P
=
2
3...
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