Wave Function Collapse: Quantum Mechanics by Griffith

[nouveau_riche]

i was going through the quantum mechanics book by griffith and on the very first chapter i read that the wavefunction of the quantum particle collapse on measurement. and if the interval between the succesive measurement is shorter the particle will be found at the very same location.


the questions that i want to ask is:

does the collapse happen only in measurement and if i want to observe the quantum effect without measuring it, what will i see?

 

[bhobba]

I am not sure in this context there is a difference between observe and measure.

The biggest bug bear with QM is the fact all it predicts is the probabilities of the outcome of an observation (measurement or whatever). That's all a quantum state is - a device for predicting such things if you were to measure it. What properties it has, other than this codification of what would happen if you observe it, it is silent about. In particular it says nothing about any properties not related to an actual physical observation.

I have Griffiths book at it is OK but it is very weak on explaining exactly what QM is about. I suggest reading Hugh's - Structure and Interpretation Of Quantum Mechanics in parallel or as pre-reading:
https://www.amazon.com/dp/0674843924/?tag=pfamazon01-20

But when you are finished both I suggest Ballentine - QM - A Modern Introduction. It is much much better going from the math to the postulates to the interpretation to the applications. I would suggest it straight up but it is a graduate level book and its best to have some prior background.

Thanks
Bill

 

[nouveau_riche]

I am not sure in this context there is a difference between observe and measure.

The biggest bug bear with QM is the fact all it predicts is the probabilities of the outcome of an observation (measurement or whatever). That's all a quantum state is - a device for predicting such things if you were to measure it. What properties it has, other than this codification of what would happen if you observe it, it is silent about. In particular it says nothing about any properties not related to an actual physical observation.

I have Griffiths book at it is OK but it is very weak on explaining exactly what QM is about. I suggest reading Hugh's - Structure and Interpretation Of Quantum Mechanics in parallel or as pre-reading:
https://www.amazon.com/dp/0674843924/?tag=pfamazon01-20

But when you are finished both I suggest Ballentine - QM - A Modern Introduction. It is much much better going from the math to the postulates to the interpretation to the applications. I would suggest it straight up but it is a graduate level book and its best to have some prior background.

Thanks
Bill

but observation can differ from measurement, in case observation ou collapse the wavefunction, doesn't that violate uncertainity principle.
i have also read that a particle is found to be at a place when looked for it,everytime then how do we know it has probabilities for various regions.

 

[bhobba]

but observation can differ from measurement, in case observation ou collapse the wavefunction, doesn't that violate uncertainity principle.
i have also read that a particle is found to be at a place when looked for it,everytime then how do we know it has probabilities for various regions.

In the context of QM observation and measurement are the same thing. Both collapse the wavefunction. This has nothing to do with the uncertainty principle which is another issue. A measurement is simply a careful observation where you likely assign a real number to the outcome such as position or whatever. An observation is something usually not as formal where you might simply say I got outcome 1, 2 or whatever. It really is simply a semantic issue - nothing to do with the basic fact you need to interact with the system in some way. The two are in fact virtually always used interchangeably and in fact no difference is usually meant.

A QM particle does not have a position until it is observed (or measured - in this contest its interchangeable) to have a position - in between measurements what properties it has such as position, momentum, spin or whatever is anyone's guess - the theory is silent about it - or rather it would be more correct to say that depends on what interpretation you subscribe to.

The reason you know probabilities is that is what the system state tells us (not directly - it is encoded in the formula the average of the outcome of any observation is trace(pR) where p is the state and R the observable representing the observation you are doing) - and that's all - it does not tell us anything other than the probabilities of the outcome of observations if you were to observe it. What properties it has independent of observation it does not tell us.

Thanks
Bill

 

[sugeet]

consider 5 cups and a coin, the five cups represent possible states, the coin is say an electron, there is a probabity for the electron in each cup, they need not be equal, nevertheless, the electron keeps jumping from one to another, not literally, but in some sense, (in reality it is there everywhere(all ossible states) as a wave), when you make a measurement, you locate it in a particular state, that`s collapse, as I understand to a beginer

 

[bhobba]

Your understanding as a beginner is incorrect. Consider an observation on a system that has n outcomes. What QM says is all we can predict is the probability of one of those outcomes - that's it - that's all. It does not say the coins are jumping or anything like your analogy - it says nothing at all about what the system is doing in any kind of visualisable sense. What it is doing prior to the observation is not known except we can assign the system something called the state that allows us to predict the probabilities of the outcome of the observation. Once it is observed we know it has some outcome and from physical continuity it is assumed if you observed it immediately afterwards it will definitely give that outcome again. Thus it has changed from a state that gives probabilities of a lot of different possible outcome to one that gives one outcome with 100% certainty. This is the collapse of the wavefunction issue - the state instantaneously and discontinuously changes to another state due to observation. If it is an issue for you depends on your interpretation. If you hold to the Ensemble interpretation like I do, or even the bog standard Copenhagen interpretation, it is not an issue because the state is simply the codification of knowledge about the system that allows you to predict probabilities - this is similar to the probabilities assigned to a coin when you toss it - it is simply a theoretical device that allows you to predict likely outcomes - it does not exist out there in any real sense like say an electric field does. Issues do remain and IMHO decoherence solves the important ones such as does it reveal a pre existing property (if you take into account decoherence it does) but it does not tell you what that property is - it only gives probabilities - which to some people is a problem.

May I suggest you actually study a textbook? If you have a HS knowledge of math and a smattering of calculus I suggest - Hughs - The Structure and Interpretation of QM:
https://www.amazon.com/dp/0674843924/?tag=pfamazon01-20

Thanks
Bill

 

[sugeet]

"Once it is observed we know it has some outcome and from physical continuity it is assumed if you observed it immediately afterwards it will definitely give that outcome again."

I don`t agree with this, do you mean that each measurement depends on previous measurement, measurement is a process of localizing our particle. By measuring we are fixing the eigen-state, we are forcing the particle to fall into one of the states, I do not mean that we have the knowledge of the particle before measuring, but you can`t deny that we assume it to be in any of its eigen states and any linear combination of them, but in reality, I mean when measured, it has to be in an eigen state, so it collapses or is forced to be in that state.

 

[bhobba]

What I am saying is that we do not expect the system to change much in an infinitesimal instant of time so if you measure it and it gave a certain outcome and you do exactly the same measurement again an infinitesimal instant later you will get exactly the same outcome - that is more or less the definition of continuity. Nothing much to it really.

Thanks
Bill

 

[mfb]

"Once it is observed we know it has some outcome and from physical continuity it is assumed if you observed it immediately afterwards it will definitely give that outcome again."

I don`t agree with this, do you mean that each measurement depends on previous measurement, measurement is a process of localizing our particle. By measuring we are fixing the eigen-state, we are forcing the particle to fall into one of the states, I do not mean that we have the knowledge of the particle before measuring, but you can`t deny that we assume it to be in any of its eigen states and any linear combination of them, but in reality, I mean when measured, it has to be in an eigen state, so it collapses or is forced to be in that state.

The quote probably refers to the quantum zeno effect - you can prevent some specific systems from changing (or at least reduce the rate) by observing them frequently.