How do I derive the general expression for delta p times delta x?

In summary, the general expression for delta p times delta x is given by the formula ΔpΔx = ħ/2 and is derived using the Heisenberg uncertainty principle. This expression reveals a fundamental limit to the precision of measuring the momentum and position of particles due to the probabilistic nature of quantum mechanics. It can be applied to all particles and has practical applications in fields such as electronics, quantum computing, nanotechnology, and medicine.
  • #1
Hey guys!
How do I derive the general expression for delta p times delta x which is the exception value in the harmonic oscillator. I am supposed to establish delta p and delta x as operators and the express those operators by raising and lowering operators.
 
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  • #2
montecarlous said:
I am supposed to establish delta p and delta x as operators

Is this a homework problem? If so, you need to post it in the homework forum and fill out the template.
 
  • #3
Moderator's note: Thread level changed to "I".
 

1. What is the general expression for delta p times delta x?

The general expression for delta p times delta x is given by the formula ΔpΔx = ħ/2, where Δp represents the uncertainty in momentum and Δx represents the uncertainty in position.

2. How is the general expression for delta p times delta x derived?

The general expression for delta p times delta x is derived using the Heisenberg uncertainty principle, which states that the product of the uncertainties in momentum and position of a particle must be greater than or equal to a certain constant value, known as the reduced Planck's constant (ħ).

3. What does the general expression for delta p times delta x reveal about the behavior of particles?

The general expression for delta p times delta x reveals that there is a fundamental limit to the precision with which we can measure the momentum and position of a particle simultaneously. This is due to the inherent probabilistic nature of quantum mechanics.

4. Can the general expression for delta p times delta x be applied to all particles?

Yes, the general expression for delta p times delta x can be applied to all particles, including subatomic particles like electrons and larger particles like atoms and molecules. It is a fundamental principle of quantum mechanics that applies to all systems at the microscopic level.

5. How is the general expression for delta p times delta x used in practical applications?

The general expression for delta p times delta x is used in various practical applications, such as in the design of electronic devices and in quantum computing. It also has implications in fields such as nanotechnology and medicine, where precise measurements of subatomic particles are necessary.

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