Hitachi High-Tech develops high-speed deterioration diagnosis method for lithium-ion batteries
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The evaluation method developed by Hitachi High-Tech this time is said to be able to instantly analyze changes over time such as current and voltage, and make a diagnosis in a few seconds to 2 minutes.
Hitachi High-Tech will instantly evaluate the performance deterioration and remaining life of lithium-ion batteries in use and used on the 20th. → Continue reading
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Wikipedia related words
If there is no explanation, there is no corresponding item on Wikipedia.
Time evolutionWhat is (Jikan Hatten)?TimeThe physical system changes as the process progresses.
For example,Classical mechanicsIs a form ofNewtonian mechanicsThen, time evolutionNewton's equation of motionExpressed by. Equivalent to thisHamiltonian mechanicsThen, time evolutionCanonical equationExpressed inLagrangian mechanicsThen, time evolutionEuler-Lagrange's equation of motionIt is expressed by.
Quantum theorySo no matter how the sameStatusPrepare a physical quantity in the same way (Observable), The measured values are different for each measurement. In the measurement of quantum theory, it is the "probability distribution of measured values" that is uniquely determined when the state and the observable are determined. Therefore, in quantum theory, the theory is constructed based on the "probability distribution of measured values". Conversely, any theory can be made as long as the obtained "probability distribution of measured values" is the same (in fact,operatorFormat orPath integralTheories such as form are made).
Therefore, in quantum theory, the time evolution of the system is also defined using the probability distribution of the measured values. The time evolution of the system in quantum theory is that the probability distribution of the measured values obtained differs depending on the time of measurement.
The time evolution formulation can be any method as long as it gives the same probability distribution of measurements. There are the following three typical methods. All three methods等価.
- Schrodinger picture : StatusI think that changes with time. in this caseSchrodinger equationIs the basic equation for time evolution.
- Heisenberg picture : ObservableI think that changes with time. in this caseHeisenberg equation of motionIs the basic equation for time evolution.
- Interaction picture: I think that both the state and the observable change with time. In this case, two equations representing time evolution appear. Of the two, the equation for the time evolution of the state is called the Tomonaga-Schwinger equation.
Time evolution operator
For closed systems, the timet State inIs the timet State at = 0TheUnitary transformationIt was done. In other wordsvectorThe length and inner product of are not changed over time (this is naturally derived from the basic equation of time evolution, such as Schrodinger equation).
This unitary transformation is oneHilbert spaceSince it is a unitary transformation within, it can be written by the operator on the Hilbert space. thisTime evolution operatorCalled (also called a time propulsion operator)Write.
This satisfies the following propertiesUnitary operator.
The equation that the time evolution operator must satisfy is from the Schrodinger equation.
Is. HamiltonianIn each case represented by, this formula is the initial conditionWhen solved as, a concrete form of the time evolution operator representing the time evolution in that case is obtained.
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