Continuous simultaneous measurement of position and momentum of a particle

Gampel, Filip; Gajda, Mariusz

doi:10.1103/physreva.107.012420

Cited by 4 publications

(8 citation statements)

References 68 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This logic of the simultaneous determination of position and momentum can be represented by the diagram shown in Figure 2. It is necessary to note that until the sixties it was generally believed that it is impossible to measure two conjugate observables together, but since then the matter has not been the case: it is currently accepted that it is possible to measure two conjugate observables together [1] [69]. The emergence of the theory of the positive-operator valued measurement (POVM) is a significant example that shows the renovation in the understanding of the uncertainty principle [70] [71].…”

Section: Basic Premises Of Quantum Mechanics In Phase Spacementioning

confidence: 99%

Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space

Jongcor¹,

Kim²,

Jon³

et al. 2023

WJM

View full text Add to dashboard Cite

The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.

show abstract

Section: Basic Premises Of Quantum Mechanics In Phase Spacementioning

confidence: 99%

Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space

Jongcor¹,

Kim²,

Jon³

et al. 2023

WJM

View full text Add to dashboard Cite

show abstract

“…Here we use the theoretical model introduced by us in [45]. We assume that every measurement provides a value of position and momentum of the particle at this instant.…”

Section: Monte Carlo Dynamics Of a Wavefunctionmentioning

confidence: 99%

“…Interaction with the detectors is represented by the nonhermitian term, i 2 C † α C α . This term causes a a kind of 'accummulation' of the wavefunction around the detector positions in phase space [45]. In each timestep δt every detector contributes to the particle wavefunction, ϕ, by an amount proportional to ∝ − 1 2 γδt⟨x|α⟩⟨α|ϕ⟩.…”

Section: Monte Carlo Dynamics Of a Wavefunctionmentioning

confidence: 99%

See 1 more Smart Citation

On Repeated Measurements of a Quantum Particle in a Harmonic Potential

Gampel

Gajda

2023

Acta Phys. Pol. A

View full text Add to dashboard Cite

We study evolution of a quantum particle in a harmonic potential whose position and momentum are repeatedly monitored. A back-action of measuring devices is accounted for. Our model utilizes a generalized measurement corresponding to the Positive Operator-Valued Measure. We assume that upon measurement the particle's wavefunction is projected onto one of possible detector states depending on the observed result. We chose these post-measurement states to be moving Gaussian wavepackets. The Wave Function Quantum Monte-Carlo formalism is used to simulate single quantum trajectories of the particle. We show how classical trajectories emerge in course of observation and study in detail dispersion of position and momentum of the particle.

show abstract

“…The classical limit of quantum mechanics is still a vivid subject of investigation (see, e.g., [19]). One of the recently discussed problems in this area relates to the successive measurements of particle position and detection of the trajectory.…”

Section: Introductionmentioning

confidence: 99%

Electron Localization in Rydberg States

Mostowski

Pietraszewicz

2023

Acta Phys. Pol. A

View full text Add to dashboard Cite

We discuss the possibility of localizing an electron in a highly excited Rydberg state. The second-order correlation of emitted photons is the tool for the determination of electron position. This second-order correlation of emitted radiation and, therefore, the correlation of operators describing the acceleration of the electron allows for a partial localization of the electron in its orbit. The correlation function is found by approximating the transition matrix elements by their values in the classical limit. It is shown that the second-order correlation, depending on two times, is a function of the time difference and is a periodic function of this argument with the period equal to the period of the corresponding classical motion. The function has sharp maxima corresponding to large electron acceleration in the vicinity of the "perihelion." This allows the localization of the electron in its consecutive approach to the perihelion point.

show abstract

Continuous simultaneous measurement of position and momentum of a particle

Cited by 4 publications

References 68 publications

Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space

Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space

On Repeated Measurements of a Quantum Particle in a Harmonic Potential

Electron Localization in Rydberg States

Contact Info

Product

Resources

About