Quantum measurement of energy

[causalset]

I would like to know, does anyone know of specific examples of quantum measurement of energy? The reason I am asking is that anything that is observed is ultimately in a position space as opposed to momentum space (for example, it might be specific position of the errow of a measurement device). So, does energy measurement ultimately involve position measurement? If so, how can we get around the uncertainty relations?

I also have a related question: how is it possible to measure an energy of a single particleanyway? For one thing, its energy is very small, so how can it be suffi cient to cause something classically observed. Also, in light of second quantization, a particle can decay any time.

 

[ZapperZ]

My avatar is a CCD image of photoelectrons emitted from a material. The vertical axis is energy, the horizontal axis is momentum. It measures the band dispersion of the material in a particular crystal symmetry direction using angle-resolved photoemission technique.

The energy is measured, using this instrument, using a series of electrostatic "lenses". But this is similar to putting those photoelectrons (or any charge particle) into a dipole magnet and bending the trajectory. By knowing the strength of the field, and the amount that the particle got bent in the field (i.e you look at a screen and the position where the particle hits), you can measure its energy. This is a technique that we often used in electron particle accelerator.

Zz.

 

[Entropia]

I can provide some information and insights on quantum measurement of energy. First of all, there are indeed specific examples of quantum measurement of energy. One example is the measurement of the energy levels of an atom using spectroscopy techniques. Another example is the measurement of the energy of a photon using photodetectors.

In quantum mechanics, energy is represented by the Hamiltonian operator, and its measurement involves the application of this operator on the quantum state of the system. This measurement does not necessarily involve position measurement. In fact, the energy of a system can be measured using a variety of different observables, such as momentum or angular momentum.

However, it is true that in order to observe the energy of a system, we need to interact with it in some way. This interaction can lead to the disturbance of the system, which is where the uncertainty principle comes into play. The uncertainty principle states that there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously.

In terms of measuring the energy of a single particle, it is indeed a challenging task. However, advancements in technology have allowed us to develop highly sensitive detectors and techniques that can measure the energy of individual particles. Also, as you mentioned, in quantum mechanics, a particle can exist in a state of superposition, meaning it can have multiple energy levels simultaneously. In this case, the energy of the particle can be measured by observing the probability of it being in a certain energy state.

In conclusion, quantum measurement of energy does not necessarily involve position measurement, and the uncertainty principle plays a crucial role in understanding the limitations of energy measurement. While measuring the energy of a single particle may be challenging, advancements in technology and quantum mechanics have allowed us to overcome some of these obstacles.