- #1
luxxio
- 44
- 0
it is possible to build a non trivial operator which the mean value is always zero?
no. a constant will not return a zero mean value.xepma said:That would mean it's mean value is always a constant.
this is not true. a little example:xepma said:I was referring to the more general case: what does it mean to have an operator O which always has a mean value equal to some constant C?
That means that <O> = C, irrespective of the state. Therefore, the operator can be represented by a the constant C times the identity opeator 1, so O = C*1. This leas to:
<O> = C<1> = C, which is what we desire.
You're asking for the special case when C=0. This automatically leads to the trivial operator 0.
CPL.Luke said:I'm pretty sure that in general the only operator that could always be guarenteed to commute with any hamiltonian would be the hamiltonian itself or a constant, thus the only operators which have a constant mean value in time are the hamiltonian and some constant operator.
The zero mean value operator, also known as the mean operator, is a mathematical function that calculates the average value of a set of numbers by summing all the values and dividing by the total number of values.
The zero mean value operator is used to remove any bias or offset from a set of data. It is commonly used in signal processing and data analysis to center the data around zero, making it easier to interpret and compare with other data sets.
To calculate the zero mean value operator, we first sum all the values in the data set, then divide the sum by the total number of values. This gives us the mean or average value of the data set. Then, we subtract this mean value from each individual value in the data set, resulting in a new data set with a mean of zero.
Using the zero mean value operator allows for easier comparison and analysis of data sets, as it removes any bias or offset. It also helps to reduce the impact of outliers or extreme values in the data, making it a more robust measure of central tendency.
One limitation of the zero mean value operator is that it assumes the data is normally distributed. If the data is not normally distributed, the mean may not be a representative measure of the central tendency. It also does not take into account the shape of the data distribution, so it may not be suitable for all types of data.