Does the n=0 State in a Quantum Box Violate the Uncertainty Principle?

  • Thread starter pivoxa15
  • Start date
  • Tags
    State
In summary, the conversation discusses the relationship between the state n=0 for a particle in a 1D box and the uncertainty principle, delta(x)delta(p)>=h(bar)/2. The participants mention trying to substitute different relationships and computing the uncertainties for each variable, x and p_{x}, while knowing the wavefunction. They also discuss the energy spectrum for the particle and its relationship to the uncertainty principle. The conversation ends with a question about a quantifiable way to express the argument.
  • #1
pivoxa15
2,255
1
How would you go about this question?

Show that by allowing the state n=0 for a particle in a 1D box will violoate the uncertainty principle, delta(x)delta(p)>=h(bar)/2

I have tried to substitute all sorts of different relationships but do seem to get anywhere. I have showed that E=0 for a ground state electron but can't seem to relate it to the uncertainty principle.
 
Physics news on Phys.org
  • #2
You just have to compute the uncertainties for each variable, x and p_{x}, knowing the wavefunction.

Daniel.
 
  • #3
dextercioby said:
You just have to compute the uncertainties for each variable, x and p_{x}, knowing the wavefunction.

Daniel.


If we allow n=0, the wavefunction will cease to exist hence the particle will cease to exist. Hence momentum and position of a particle does not exist or could you say 0. Hence any change in the n=0 state, the particle will continue to cease to exist. In this way the HU principle will not be satisfied. But my argument is pretty vague. Is there a quantifiable way to express this?
 
  • #4
What's the energy spectrum for the particle...?

Daniel.
 
  • #5
What do you mean by the energy spectrum?

Do you mean the energy levels?
At n=0, Energy=0.
At other levels, Energy=n^2(pie)^2(hbar)^2/(2mL^2)

But how does it relate to the UC?
 

FAQ: Does the n=0 State in a Quantum Box Violate the Uncertainty Principle?

What is the Heinsenberg uncertainty principle?

The Heinsenberg uncertainty principle is a fundamental concept in quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a particle. In other words, the more accurately we know the position of a particle, the less accurately we can know its momentum, and vice versa.

What is the significance of the n=0 state in the Heinsenberg uncertainty principle?

The n=0 state, also known as the ground state, is the lowest energy state of a quantum system. In the context of the Heinsenberg uncertainty principle, it is used to represent the minimum uncertainty that can exist between a particle's position and momentum. This means that the n=0 state has the most well-defined position and momentum possible for a particle.

How does the Heinsenberg uncertainty principle relate to the concept of wave-particle duality?

The Heinsenberg uncertainty principle is closely related to the concept of wave-particle duality, which states that particles can exhibit both wave-like and particle-like behavior. The uncertainty principle arises from the wave-like nature of particles, as it is impossible to accurately measure both the position and momentum of a wave at the same time.

Can the Heinsenberg uncertainty principle be violated or overcome?

No, the Heinsenberg uncertainty principle is a fundamental law of quantum mechanics and cannot be violated or overcome. It is a consequence of the probabilistic nature of quantum particles and the limitations of measuring their properties.

How does the Heinsenberg uncertainty principle impact our daily lives?

The Heinsenberg uncertainty principle may seem like a concept that only applies to the microscopic world, but it actually has important implications for our daily lives. It explains why we cannot accurately predict the exact position and momentum of macroscopic objects and why there will always be a degree of uncertainty in our measurements. It also plays a crucial role in many modern technologies, such as transistors, lasers, and MRI machines.

Similar threads

Do Coherent States Imply 0 Energy Uncertainty?
Replies
5
Views
1K
Exploring the Time-Energy Uncertainty Relation to Solve a Schrodinger Equation
Replies
2
Views
1K
Proton in a 1D Box: Energy, Probability, Speed
Replies
24
Views
2K
I Volume of momentum space of an ideal gas
Replies
8
Views
677
Use the uncertainty principle for momentum vs. position to e
Replies
2
Views
1K
What Is Energy Degeneracy in a Cubical Box?
Replies
8
Views
1K
Differentiation of functional integral (Blundell Quantum field theory)
Replies
1
Views
1K
Rigid Box Particle and Heisenberg Principle
Replies
8
Views
4K
Uncertainty Principle: Computing Δx & Δp for a Particle in a 1D Box
Replies
4
Views
3K
Uncertainty principle for time-energy & momentum-position
Replies
5
Views
3K

Hot Threads

Recent Insights

Back
Top