Energy time uncertainty12/16/2023 ![]() If you're focusing on trying to watch the speed, then you may be off a bit when measuring the exact time across the finish line, and vice versa. ![]() The physical nature of the system imposes a definite limit upon how precise this can all be. The minimum uncertainty in energy E is found by using the equals sign in E t h /4 and corresponds to a reasonable choice for the uncertainty in time. The Schrdinger equation is the fundamental equation of wave quantum mechanics. The average kinetic energy is on the order of T (p)2/2m, and the average potential energy is. We'll see the car touch the finish line, push the stopwatch button, and look at the digital display. The energy-time uncertainty principle expresses the experimental observation that a quantum state that exists only for a short time cannot have a definite energy. Then the uncertainty in its momentum is p /x about p 0. ![]() In this classical case, there is clearly some degree of uncertainty about this, because these actions take some physical time. We measure the speed by pushing a button on a stopwatch at the moment we see it cross the finish line and we measure the speed by looking at a digital read-out (which is not in line with watching the car, so you have to turn your head once it crosses the finish line). We are supposed to measure not only the time that it crosses the finish line but also the exact speed at which it does so. ![]() Let's say that we were watching a race car on a track and we were supposed to record when it crossed a finish line. Though the above may seem very strange, there's actually a decent correspondence to the way we can function in the real (that is, classical) world. ![]()
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