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How would the probability distribution (|psi|^2) look for a Newtonian particle if it were confined in a box?
What is "n" in Newtonian Mechanics ??How do you reconcile this with Newtonian Mechanics for high n?
A Newtonian Probability Distribution is a mathematical representation of the probability of a random variable occurring within a given range of values. It follows the principles of Newtonian physics, where all possible outcomes have an equal chance of occurring.
The key characteristics of a Newtonian Probability Distribution include a symmetrical bell-shaped curve, with the mean, median, and mode all located at the center of the distribution. It also follows the 68-95-99.7 rule, where approximately 68%, 95%, and 99.7% of the data falls within one, two, and three standard deviations from the mean, respectively.
A discrete Newtonian Probability Distribution is used for variables that can only take on specific, finite values, while a continuous Newtonian Probability Distribution is used for variables that can take on any value within a given range. Discrete distributions are represented by histograms, while continuous distributions are represented by smooth curves.
The shape of a Newtonian Probability Distribution is affected by changes in the mean and standard deviation. An increase in the mean will shift the distribution to the right, while an increase in the standard deviation will result in a wider and flatter curve. Likewise, a decrease in the mean will shift the distribution to the left, while a decrease in the standard deviation will result in a narrower and taller curve.
The central limit theorem states that the sum of a large number of independent and identically distributed random variables will follow a normal distribution, regardless of the underlying distribution of the individual variables. This means that many real-world phenomena can be modeled using a Newtonian Probability Distribution, making it a widely used tool in various fields of science and statistics.