# Meaning of zero probability density

• xfshi2000
In summary, in quantum mechanics it's a bit ill-posed to ask if a particle ever arrives' somewhere. The meaningful thing to ask is whether or not you observe the particle. Zero probability density indeed means zero chance of observing the particle in that state (e.g. at that position). It is less meaningful to ask whether the particle actually "does" pass through that point. The probability density doesn't say anything about how a particle got to the position you're observing; e.g. it doesn't tell you if a particle passes through a given point unobserved en route to being observed elsewhere.
xfshi2000
Hi
I have a question about zero point of probability density of particle. In general we say if probability density is zero at a certain position, the particle never arrive there. But I also read some post in this forum. They said zero probability density means you have zero chance of seeing the particle. It doesn't mean the particle never arrive there. Only because of wave function interference, we have zero chance to see them. For example, oscillator excited state, there are several nodes in the wave function. In real world, it still pass through the zero probability density position. Where I use inaccurate word, there is no accurate position measurement. Another example is double slit experiment. We see alternate bright band and dark band in the screen. Dark band means that we cannot see the photon reach those places but photon really visit there. Because of interference of wave function, we have no chance to see them. Is my understanding right? if wrong, where does I make a mistake? thanks

Hi xfshi, in quantum mechanics it's a bit ill-posed to ask if a particle ever arrives' somewhere. The meaningful thing to ask is whether or not you observe the particle. Zero probability density indeed means zero chance of observing the particle in that state (e.g. at that position).

It is less meaningful to ask whether the particle actually "does" pass through that point. The probability density doesn't say anything about how a particle got to the position you're observing; e.g. it doesn't tell you if a particle passes through a given point unobserved en route to being observed elsewhere.

This is one of the weird and cute features of quantum physics.

JosephButler said:
Hi xfshi, in quantum mechanics it's a bit ill-posed to ask if a particle ever `arrives' somewhere. The meaningful thing to ask is whether or not you observe the particle. Zero probability density indeed means zero chance of observing the particle in that state (e.g. at that position).

It is less meaningful to ask whether the particle actually "does" pass through that point. The probability density doesn't say anything about how a particle got to the position you're observing; e.g. it doesn't tell you if a particle passes through a given point unobserved en route to being observed elsewhere.

This is one of the weird and cute features of quantum physics.

Thank you for your reply. I agree with you. As I know there are infinite paths for particle from one position to another position(path integral). Classical path is the one with maximum probability. We indeed have no chance to observe it at zero probability density at a node point. But we don't know whether or not it pass through that specific point. thanks again.

## 1. What is the meaning of zero probability density?

Zero probability density refers to a situation where the likelihood of a particular event occurring is extremely low or impossible. It is represented by the value 0 on a probability density function, which shows the distribution of probabilities for a given set of data.

## 2. Is zero probability density the same as impossible?

No, zero probability density does not necessarily mean that the event is impossible. It simply means that the likelihood of it occurring is extremely low. It is important to note that some events with a probability density of 0 may still occur, albeit rarely.

## 3. How is zero probability density calculated?

Zero probability density is calculated by taking the limit of the probability of an event as the number of possible outcomes approaches infinity. This is represented by the equation P(x) = 0/∞, where P(x) is the probability of the event and ∞ is the number of possible outcomes.

## 4. What are some examples of events with zero probability density?

Some examples of events with zero probability density include flipping a coin and getting heads and tails at the same time, rolling a die and getting a number greater than 6, and choosing a random number between 1 and 10 and getting 11. These events are possible, but their probability is extremely low.

## 5. Why is zero probability density important in science?

Zero probability density is important in science because it helps us understand and make predictions about the likelihood of certain events occurring. It also allows us to identify and analyze rare events that may have significant impacts on our understanding of the world.

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