Timeline for Common eigenstate of incompatible observables
Current License: CC BY-SA 4.0
7 events
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| Apr 23, 2022 at 21:48 | comment | added | SolubleFish | Actually, an eigenvector cannot be zero, by definition. Two observables are compatible iff they commute, which is equivalent to them sharing a basis of common eigenstates. The general statement on pairs of incompatible observables is just the negation of the previous sentence. | |
| Apr 23, 2022 at 20:28 | comment | added | AfterShave | Okay I wasn't entirely correct. Two incompatible observables cannot share a complete set of eigenstates. It's possible to have two incompatible observables share a common eigenvector, or even several but they cannot form a complete basis. For example, the zero vector is an eigenstate of any operator. | |
| Apr 23, 2022 at 19:19 | comment | added | som | @AfterShave, If it is impossible then isn't it sufficient to say that existence of ANY one common eigenstate is sufficient to guarantee compatibility of physical observables? Requirement of a whole bunch of common eigenbasis seems over-conditioned then. | |
| Apr 19, 2022 at 7:11 | history | edited | SolubleFish | CC BY-SA 4.0 |
added 989 characters in body
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| Apr 19, 2022 at 6:52 | comment | added | AfterShave | It's not possible for two incompatible observables to have a common eigenstate. | |
| Apr 19, 2022 at 6:50 | comment | added | som | Ok, I understand. It would be helpful if you provide particular example of two incompatible physical observable having such common eigenstate | |
| Apr 19, 2022 at 6:40 | history | answered | SolubleFish | CC BY-SA 4.0 |