/The probability density does not goto zero at the nodes if

In summary, the probability density is a measure of the likelihood of a continuous random variable taking on a specific value within a given range. The nodes in probability density refer to the points on the curve where the value of the probability density function is equal to zero, but the probability density does not go to zero at these points due to the extremely small probability of the variable taking on a value exactly at the node. The probability density at the nodes is typically calculated using the limit of the probability density function. If the probability density does not go to zero at the nodes, it means that the variable has a non-zero probability of taking on a value at the node, which may require further analysis to understand the implications.
  • #1
dpa
147
0
///
The probability density does not go
to zero at the nodes if relativistic
effects are taken into account.
///
src=wikipedia, particle in a box.
///
so does it mean energy levels/atomic orbitals are not necessarily discrete and that atom has to be remodeled.
***pardon my ignorance if I am wrong. I am really amateur.
 
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  • #2


dpa said:
so does it mean energy levels/atomic orbitals are not necessarily discrete and that atom has to be remodeled.

Naa, it just means that when you take relativistic effects into account it effects the probability distributions.
 

1. How is the probability density defined?

The probability density is a measure of the likelihood of a continuous random variable taking on a specific value within a given range. It is represented by a curve on a graph, where the area under the curve within a certain interval represents the probability of the variable falling within that interval.

2. What are the nodes in probability density?

The nodes in probability density refer to the points on the curve where the value of the probability density function is equal to zero. These points indicate where the probability of the variable taking on a specific value is zero.

3. Why doesn't the probability density go to zero at the nodes?

The probability density does not go to zero at the nodes because the probability of the variable taking on a value exactly at the node is extremely small. As a result, the probability density is not defined at these points and remains non-zero.

4. How is the probability density calculated at the nodes?

The probability density at the nodes is typically calculated using the limit of the probability density function as the variable approaches the node from either side. This limit is equal to zero, but the actual value at the node is undefined.

5. What does it mean if the probability density does not go to zero at the nodes?

If the probability density does not go to zero at the nodes, it means that the variable has a non-zero probability of taking on a value at the node. This could be due to the nature of the variable or the underlying distribution, and further analysis may be needed to understand the implications of this behavior.

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