Table of Contents
- 1 Can position and momentum be measured simultaneously?
- 2 Why it is impossible to measure both position and momentum simultaneously?
- 3 Why can we not know the position and momentum of an electron at any given moment?
- 4 Is it possible to measure the energy and the momentum of a particle simultaneously with arbitrary precision?
- 5 What is the uncertainty associated with momentum when position is measured with absolute accuracy?
Can position and momentum be measured simultaneously?
You cannot measure both position and momentum simultaneously with arbitrary precision for a quantum (very very small) object. The more precisely you pin down its location, the more uncertain its momentum becomes, and vice versa.
Why it is impossible to measure both position and momentum simultaneously?
The Heisenberg uncertainty principle states that the exact position and momentum of an electron cannot be simultaneously determined. This is because electrons simply don’t have a definite position, and direction of motion, at the same time!
Why can we not know the position and momentum of an electron at any given moment?
Gamma rays are really high energy (short wavelength – that is how the “see” an electron). Since you can only “see” electrons with super high energy light, the “seeing” process actually changes the momentum of the electron and sends it flying. So you can’t know both position and momentum with accuracy.
Can an electron’s position and momentum be known precisely?
The uncertainty principle says that we cannot measure the position (x) and the momentum (p) of a particle with absolute precision. Seeing a subatomic particle, such as an electron, is not so simple.
What is the uncertainty in determining position and momentum simultaneously?
The uncertainty principle is alternatively expressed in terms of a particle’s momentum and position. The momentum of a particle is equal to the product of its mass times its velocity. Thus, the product of the uncertainties in the momentum and the position of a particle equals h/(4π) or more.
Is it possible to measure the energy and the momentum of a particle simultaneously with arbitrary precision?
The answer goes to the very heart of quantum mechanics. It turns out that energy and position are what we call noncommuting variables, in the sense that they cannot simultaneously be measured to arbitrary precision.
What is the uncertainty associated with momentum when position is measured with absolute accuracy?
Strategy. The uncertainty in position is the accuracy of the measurement, or Δx = 0.0100 nm. Thus the smallest uncertainty in momentum Δp can be calculated using ΔxΔp≥h4π Δ x Δ p ≥ h 4 π .