Recent content by charlesworth

Thanks to both of you, that's very helpful. The 2x2 examples are good, but using higher dimensional Pauli matrices is more satisfying; thanks Sando. I found a complete answer to my question in Gantmacher's text "The theory of matrices" (chapter VIII, section 8) which gives a complete...

I'd like to do one of two things: 1: Find an example of a non-diagonal matrix whose matrix exponential (defined in terms of series) is diagonal. 2: Prove that no such examples exist. I'm working with matrices over the complex field. My gut tells me that 2 is the way to go. I'd really...

I suppose I am always reluctant to admit that I know anything at all about what nature actually is. But I'm happy so long as people are thinking carefully about the physical conclusions they draw from the math, and not taking anything for granted.

What we choose to call things is often arbitrary. The "Robertson Inequality" and the "Heisenberg Inequality" were simply names I learned first in one of my undergrad QT courses; when someone mentions the Heisenberg inequality to me, I wait for context to decide what they mean; the two...

I keep hearing jargon like "the algebra generated by the hamiltonian", and I'd like to get to the bottom of it. Given a set of hamiltonians, does the "algebra that they generate" refer to the unitaries that they generate and their subsequent combinations? Or does it refer to the hamiltonians...

It is important to understand the difference between what can be called the Robertson inequality, and the Heisenberg inequality. It seems that these two notions have been mixed up in the above posts. The Robertson inequality refers to an inequality involving the expectation value of the...

Hi, I'd like to figure out the amount of heat lost in the kinematic action of putting your foot on the ground while walking. I'm not interested in the diffussion of body heat through the shoe or anything, just the heat energy released by the impact itself. I know this is obscure, and probably...

Suppose a constant volume of water is being heated up by a constant amount of power. After some time it is noted that the rate of change of temperature is slowing down. (In this scenario, assume all temperatures to be between 10 and 90 degrees Celcius) What would cause this non-linear...