Then the uncertainty in its momentum is p /x about p 0. Details of the calculation: Assume the uncertainty in the position of the electron is x about x 0. The physical nature of the system imposes a definite limit upon how precise this can all be. The uncertainty principle Reasoning: We are asked to use the uncertainty relation, x p, to estimate of the ground state energy of the harmonic oscillator. We'll see the car touch the finish line, push the stopwatch button, and look at the digital display. In this classical case, there is clearly some degree of uncertainty about this, because these actions take some physical time. In the Clifford algebra setting we propose two forms of uncertainty principle for spherical signals, of which both correspond to the strongest form of uncertainty principle for periodic signals. In plain language, thats 931.5 million eV. This paper is devoted to studying uncertainty principle of Heisenberg type for signals on the unit sphere in the Clifford algebra setting. That means its energy is about 931.5×106 eV. 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). Besides the position-momentum, another famous uncertainty is relation energy-time because the product of these two quantities (energy × time) also has the unit. The mass of our hydrogen atom is approximately 1 u 931.5×106 eV/c2. 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.
If the operators A and B are matrices, then in general AB BA. If the operators A and B are scalar operators (such as the position operators) then AB BA and the commutator is always zero. 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. The Commutator of two operators A, B is the operator C A, B such that C AB BA.
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