Is it possible for two observers to observe different wavefunctions for one electron? Suppose there are 2 scientists who have decided to measure the location of an electron at a same fixed time. Is possible that while one observes the wavepacket localized at (position=x) while the other observes the wavepacket localized at (position=y). The condition however is position x is not equal to y.Please dont confuse about the degree of localization which can be quite varying depending upon which measurement-momentum or position is given priority
:( I have little to no experience with quantum superposition and gaussian wavepackets.......kindly manage with my rough knowledge
 A: In order to observe an electron one must interact with it in some way. For example one could shine light at it so that it scattered the light, or one could arrange for it to hit something like a multi-channel array (a charge detector with many small elements). The various observers will study some sort of large-scale signal such as a current from the array or else the light hitting a camera. They will all agree on what large-scale signal was seen, and they will agree on the chain of inference which determines what information it gives about the electron. So, in summary, the answer to your question is that they all get the same answer.
A: I will confess that this I am not certain on this, as this is a quite odd question. but I have formulated what seems like a very reasonable answer. Also the very first thing to mention is that one cannot physically observe the wave-function, we can only predict how it evolves, and then measure a property of a particle, this collapsing the wave-function.
When we (in theory at least) make a measurement of position, the wave-function collapses to a Dirac-delta distribution (like a spike at where we measure the particle). Without going into the specifics, after we make the measurement, if we leave the system alone, the wave-function will spread out over time.
So lets consider what happens if we make two position measurements, at different times, but in the limit that the time goes to zero.
So if the first measurement gives $x_1$, then at some time $t$ after the measurement, we make another measurement. This measurement could be literally any value, but for a free particle will have a mean at $x_1$. And it will have some standard deviation (or uncertainty) that is greater than zero. However, as we take this $t$ to zero, that probability of the measurement being away from $x_1$ will decrease, and the standard deviation will decrease as well, until in the limit that $t=0$, the probability of the measurement being anywhere except $x_1$.
A: The OP specified that the two observers make their measurements simultaneously.  Two simultaneous measurements of the same observable are equivalent to a single measurement, which can have only one result.  Therefore, the observers must see the same result.
