Interesting Quantum Mechanics Problem

AI Thread Summary
In the discussion of a quantum mechanics problem involving a particle in a box with infinite potential outside defined boundaries, the focus is on the implications of the first excited state, which features a node at x=a/2. This node indicates a zero probability of finding the particle at that position, raising questions about how the particle can be considered to "travel" between the two halves of the box. The consensus is that in quantum mechanics, there is no traditional concept of travel; the particle exists as a probability distribution rather than a defined path. The particle can be observed with equal probability in either half of the box, and the node can be interpreted as part of the particle's wave function, representing a complex behavior that diverges from classical intuition. This highlights the non-intuitive nature of quantum mechanics, where particles are treated as mathematical entities rather than physical objects with straightforward properties.
teddy
Messages
17
Reaction score
0
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.
 
Physics news on Phys.org
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.
 
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.
 
Last edited by a moderator:

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
View full post »

Similar threads

I Why is it Impossible to Solve the Three Body Problem Analytically?
Replies
6
Views
4K
I Discussion on the probabilistic interpretation of quantum mechanics
Replies
11
Views
825
I Completeness of Eigenfunctions of Hermitian Operators
Replies
22
Views
2K
I Spontaneous Symmetry Breaking and quantum mechanics
Replies
15
Views
2K
I What does motion mean in quantum mechanics?
Replies
27
Views
3K
I QFT made Bohmian mechanics a non-starter: missed opportunities?
8
Replies
376
Views
20K
I Understanding No Energy Degeneracy in Sakurai's Quantum Mechanics
Replies
2
Views
2K
A Eigenvalue Problem of Quantum Mechanics
Replies
6
Views
2K
Can an Artist Impact Quantum Mechanics and Neurobiology?
Replies
3
Views
1K
I QED/Quantum Mechanics: Probability or Spatial Function?
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top