In quantum mechanics, the expectation value of a physical observable is determined by taking the average of the possible measurement outcomes weighted by their probabilities. The probability distribution of a quantum particle is described by its wave function, which encodes the probability amplitudes for different outcomes.
While it is true that quantum mechanics and classical mechanics (CM) are related in certain limits, such as the correspondence principle, it is important to note that gravity is not described within the framework of quantum mechanics alone. General relativity, Einstein's theory of gravity, is a classical theory that describes gravity as the curvature of spacetime.
To estimate the expectation value of quantum particles, one typically focuses on the relevant quantum mechanical principles and mathematical formalism rather than directly associating the probability curve of a photon with the gravitational field of the Earth. The behavior of quantum particles is typically studied within the context of quantum field theory, which combines quantum mechanics with special relativity and describes particles as excitations of quantum fields.
The gravitational field of the Earth can have indirect effects on quantum systems, such as gravitational time dilation or the gravitational redshift, which can be incorporated into calculations involving quantum particles in the presence of gravity. However, a direct association between the probability curve of a photon and the gravitational field of the Earth, as you suggested, is not a commonly employed method in quantum mechanics for estimating expectation values.
In summary, while gravity can have effects on quantum systems, the estimation of expectation values in quantum mechanics is primarily based on the principles and formalism of quantum mechanics itself, without a direct association with the gravitational field of the Earth.