On Thursday, February 15, 2018 at 2:46:34 AM UTC+11, Lawrence Crowell wrote:
>
> On Tuesday, February 13, 2018 at 7:45:59 PM UTC-6, Pierz wrote:
>>
>> Quantum physics tells us that anything that commutes with the hamiltonian 
>> is preserved (doesn't change), the hamiltonian being the measure of energy 
>> in a system. This has led me to understand energy as a measure of change 
>> over time in a physical system. That might be obvious, except I've never 
>> heard anybody say it quite like that - with the result that many people 
>> tend to reify energy as some kind of physical "thing". The fact that energy 
>> and matter are interconvertible has led me to the summary that change 
>> across space is matter, change across time is energy. The only problem in 
>> this picture is potential energy, which you could simply call "deferred 
>> change", but that does beg the question as to how it is deferred. I'm 
>> trying to think about this in relation to chemical energy - the potential 
>> energy held in chemical bonds. When I studied chemistry I was simply told 
>> that certain bonds are more stable and have lower energy than other bonds 
>> which are less stable and have higher energy. So energy is released when a 
>> molecule reacts with another to form a more stable compound. The reason for 
>> and nature of the stability wasn't explained. So I'm wondering, is the 
>> "potential energy" in the chemical bond actually a kind of very localised 
>> motion, with more motion occurring in high energy bonds than in lower 
>> energy ones? In other words, the energy (motion/change) is temporarily 
>> contained in the small area of the bond, thus hiding the energy it as it 
>> were from the environment? If so, then this form of potential energy is not 
>> really different in kind from other types of energy, it's just relatively 
>> isolated. If this is valid, perhaps a similar analysis of other forms of 
>> potential energy such as gravitational potential might be possible too? Can 
>> a physicist/physical chemist perhaps shed light on whether my speculation 
>> here regarding chemical energy is valid? 
>>
>
> The Hamiltonian is the generator of time development. A quantum wave 
> function  ψ(t) is pushed to the time t' > t by the operator exp(-iH(t' - 
> t)) so that ψ(t') =  exp(-iH(t' - t))ψ(t).
>
> LC
>
Yes the good ole Schrödinger equation. The fact that the Hamiltonian is the 
generator of time development *and* the operator for energy helped me to 
understand that energy is change. But I'm trying to understand something 
about the nature of the energy held in chemical bonds. A high energy 
chemical bond must have a corresponding Hamiltonian that shows some kind of 
evolution in the state of the electrons involved in the bond. The so-called 
potential energy must be represented as some kind of state evolution of the 
electrons - right?

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