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occurred Feb 27, 2019 at 0:01

Notice added Reward existing answer by Emilio Pisanty

occurred Feb 19, 2019 at 22:47

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occurred Feb 19, 2019 at 22:47

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edited Jul 5, 2018 at 14:07

Qmechanic ♦

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Is the Moyal-Liouville equation $\frac{\partial \rho}{dt\partial t}= \frac{1}{i\hbar} [H\stackrel{\star}{,}\rho]$ used in applications?

This answer by Qmechanic shows that the classical Liouville equation can be extended to quantum mechanics by the use of Moyal star products, where it takes the form $$ \frac{\partial \rho}{dt}~=~ \frac{1}{i\hbar} [H\stackrel{\star}{,}\rho]. $$$$ \frac{\partial \rho}{\partial t}~=~ \frac{1}{i\hbar} [H\stackrel{\star}{,}\rho]. $$ I've seen this mentioned as a possible classical interpretation of quantum mechanics, but I've never seen this used in anger, so I want to ask: is this representation actually useful in understanding dynamics? In what contexts does it provide insights about physical processes that are harder to obtain through alternative routes?

I'm not really looking for an exhaustive list of places where this representation turns up, but I would like to see a few representative examples to get a better feel of how it looks like in applications.

Is the Moyal-Liouville equation $\frac{\partial \rho}{dt}= \frac{1}{i\hbar} [H\stackrel{\star}{,}\rho]$ used in applications?

This answer by Qmechanic shows that the classical Liouville equation can be extended to quantum mechanics by the use of Moyal star products, where it takes the form $$ \frac{\partial \rho}{dt}~=~ \frac{1}{i\hbar} [H\stackrel{\star}{,}\rho]. $$ I've seen this mentioned as a possible classical interpretation of quantum mechanics, but I've never seen this used in anger, so I want to ask: is this representation actually useful in understanding dynamics? In what contexts does it provide insights about physical processes that are harder to obtain through alternative routes?

I'm not really looking for an exhaustive list of places where this representation turns up, but I would like to see a few representative examples to get a better feel of how it looks like in applications.

Is the Moyal-Liouville equation $\frac{\partial \rho}{\partial t}= \frac{1}{i\hbar} [H\stackrel{\star}{,}\rho]$ used in applications?

This answer by Qmechanic shows that the classical Liouville equation can be extended to quantum mechanics by the use of Moyal star products, where it takes the form $$ \frac{\partial \rho}{\partial t}~=~ \frac{1}{i\hbar} [H\stackrel{\star}{,}\rho]. $$ I've seen this mentioned as a possible classical interpretation of quantum mechanics, but I've never seen this used in anger, so I want to ask: is this representation actually useful in understanding dynamics? In what contexts does it provide insights about physical processes that are harder to obtain through alternative routes?

I'm not really looking for an exhaustive list of places where this representation turns up, but I would like to see a few representative examples to get a better feel of how it looks like in applications.

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edited Jul 5, 2018 at 12:34

Qmechanic ♦

213.1k
48
590
2.3k

Is the Moyal-Liouville equation $\frac{d\rho\partial \rho}{dt}= \frac{1}{i\hbar} [\rho\stackrel[H\stackrel{\star}{,}H]$\rho]$ used in applications?

This answer by Qmechanic shows that the classical Liouville equation can be extended to quantum mechanics by the use of Moyal star products, where it takes the form $$ \frac{d\rho}{dt}= \frac{1}{i\hbar} [\rho\stackrel{\star}{,}H]. $$$$ \frac{\partial \rho}{dt}~=~ \frac{1}{i\hbar} [H\stackrel{\star}{,}\rho]. $$ I've seen this mentioned as a possible classical interpretation of quantum mechanics, but I've never seen this used in anger, so I want to ask: is this representation actually useful in understanding dynamics? In what contexts does it provide insights about physical processes that are harder to obtain through alternative routes?

I'm not really looking for an exhaustive list of places where this representation turns up, but I would like to see a few representative examples to get a better feel of how it looks like in applications.

Is the Moyal-Liouville equation $\frac{d\rho}{dt}= \frac{1}{i\hbar} [\rho\stackrel{\star}{,}H]$ used in applications?

This answer by Qmechanic shows that the classical Liouville equation can be extended to quantum mechanics by the use of Moyal star products, where it takes the form $$ \frac{d\rho}{dt}= \frac{1}{i\hbar} [\rho\stackrel{\star}{,}H]. $$ I've seen this mentioned as a possible classical interpretation of quantum mechanics, but I've never seen this used in anger, so I want to ask: is this representation actually useful in understanding dynamics? In what contexts does it provide insights about physical processes that are harder to obtain through alternative routes?

I'm not really looking for an exhaustive list of places where this representation turns up, but I would like to see a few representative examples to get a better feel of how it looks like in applications.

Is the Moyal-Liouville equation $\frac{\partial \rho}{dt}= \frac{1}{i\hbar} [H\stackrel{\star}{,}\rho]$ used in applications?

This answer by Qmechanic shows that the classical Liouville equation can be extended to quantum mechanics by the use of Moyal star products, where it takes the form $$ \frac{\partial \rho}{dt}~=~ \frac{1}{i\hbar} [H\stackrel{\star}{,}\rho]. $$ I've seen this mentioned as a possible classical interpretation of quantum mechanics, but I've never seen this used in anger, so I want to ask: is this representation actually useful in understanding dynamics? In what contexts does it provide insights about physical processes that are harder to obtain through alternative routes?

I'm not really looking for an exhaustive list of places where this representation turns up, but I would like to see a few representative examples to get a better feel of how it looks like in applications.