Localised solution of stochastic Schrödinger equation describing simultaneous continuous measurement of position and momentum
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914038317842432 |
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| author | Bedingham, Daniel J. |
| author_facet | Bedingham, Daniel J. |
| contents | A stochastic Schrödinger equation is presented to describe simultaneous continuous measurement of the position and momentum of a non-relativistic particle. The equation is solved to yield a state localised in position and momentum contingent on the uncertainty principle. The state is understood as that to which the particle tends after a period of continuous measurement. The solution takes the form of a wave packet of fixed Gaussian shape whose centre undergoes random motion in phase space. It is shown to be locally stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11832 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localised solution of stochastic Schrödinger equation describing simultaneous continuous measurement of position and momentum Bedingham, Daniel J. Quantum Physics A stochastic Schrödinger equation is presented to describe simultaneous continuous measurement of the position and momentum of a non-relativistic particle. The equation is solved to yield a state localised in position and momentum contingent on the uncertainty principle. The state is understood as that to which the particle tends after a period of continuous measurement. The solution takes the form of a wave packet of fixed Gaussian shape whose centre undergoes random motion in phase space. It is shown to be locally stable. |
| title | Localised solution of stochastic Schrödinger equation describing simultaneous continuous measurement of position and momentum |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.11832 |