Interesting Quantum Mechanics Problem

In summary, the conversation discusses an interesting quantum mechanics problem involving a particle in a box with infinite potential. The solution to the Schrödinger equation reveals a node at x=a/2 for the first excited state, which means the particle cannot be found at that position at any time. However, the question arises of how the particle can travel between the two halves of the box without encountering the node. The answer is that in quantum mechanics, there is no well-defined path and the particle always has an equal probability of being observed in either half of the box. This may seem strange, but it is a fundamental aspect of the universe according to quantum mechanics.
  • #1
teddy
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Interesting Quantum Mechanics Problem

Suppose we have a particle in a box with infinite potential for x>a and x<0 and zero potential in between.Then by solving the schrd. equation we get a node at x= a/2 for first excited state.Which means the probability of finding the particle at x=a/2 is zero for all times if it is a stationary first excited state.
Then how does the particle travel from one half of the box to the another without encountering the node.I know there is no well defined path but still space is well-connected and have no loops or whatever. I am feeling quite uneasy regarding this.

please...enlightment.
 
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  • #2
There is no 'travel', just like you said. The particle always has an equal probability of being observed in either half of the box; you can't say it's ever in one or the other, nor that it is traveling between them.
I am feeling quite uneasy regarding this.
Welcome to the world of QM. :wink: The universe is just really weird; eventually you will get used to it.
 
  • #3
Basicly, this node IS particle itself (along with two maxima). Or consider it to be sum of two "parts" of the particle traveling in opposite directions.

Particles (=waves) are mathematical objects, and their properties do not have to be the same as properties of baseball or ocean wave.
 
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1. What is Quantum Mechanics?

Quantum Mechanics is a branch of physics that deals with the behavior and interactions of particles on a very small scale, such as atoms and subatomic particles. It describes how these particles behave and interact with each other through fundamental principles and mathematical equations.

2. What is an Interesting Quantum Mechanics Problem?

An Interesting Quantum Mechanics Problem is a problem or puzzle that challenges our understanding of the principles and theories of Quantum Mechanics. It often involves complex mathematical calculations and requires creative thinking to solve.

3. Can you provide an example of an Interesting Quantum Mechanics Problem?

One example of an Interesting Quantum Mechanics Problem is the Schrodinger's Cat thought experiment, which explores the concept of superposition and the collapse of the wave function. It asks the question of whether a cat in a sealed box can be both alive and dead at the same time.

4. How is Quantum Mechanics used in real-world applications?

Quantum Mechanics has many practical applications, such as in developing new technologies like quantum computers and encryption methods. It is also used in fields such as chemistry, material science, and engineering to understand and manipulate the behavior of particles on a molecular level.

5. Why is Quantum Mechanics important?

Quantum Mechanics is important because it provides a fundamental understanding of the behavior of particles at the smallest scale. It has revolutionized our understanding of the universe and has led to many technological advancements. It also has the potential to lead to even more groundbreaking discoveries in the future.

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