Almost all my outcomes are written in the following preprint (the lecture note of the master course in Dept of Math. Keio university).

Shiro Ishikawa,
"Linguistic Interpretation of Quantum Mechanics : Quantum language [ver.2]"

KSTS/RR-16/001 (2016, Research Report in Keio Math)

The following web-version is extracted from the above preprint.
Proofs and detailed calculations are omitted.
But many figures are added.
KSTS/RR-16/001 (2016, Research Report in Keio Math)

1.1:Quantum language

1.2(1):Axioms 1 and 2 (measurement and causality ) and interpretation:

1.2(2):Linguistic interpretation

1.2(3):Summary

1.3:Example (Hot or Cold?)

2.1: Basic structure $[{\mathcal A} \subseteq$ $ \overline{\mathcal A} \subseteq B(H)]$( General Theory)

2.2: Quantum basic structure $[{\mathcal C}(H) \subseteq$ $ B(H) \subseteq B(H)]$

2.3: Classical basic structure $[C_0(\Omega ) \subseteq$ $ L^\infty ( \Omega, \nu ) \subseteq B(H)]$

2.4: State and observable

2.5: Examples of observables

2.6: System quantity

2.7: Axiom 1 ; No science without measurements

2.8: Classicalexamples ( urn problem, etc.)

2.9: Stern=Gerlach experiment

2.10: de Broglie paradox

3.1: The linguistic interpretation

3.2: Tensor operator algebra

3.3.1: Only one observable

3.3.2: state doesnot move

3.3.3: Only one state

4.1: Kolmogorov extension theorem

4.2: The law of large numbers

4.3.1: Why is Heisenberg's uncertainty principle famous?

4.3.2: Mathematical formulation of Heisenberg's uncertainty principle

4.3.3: except approximately simultaneous measurement

4.4: EPR-paradox

4.5: Bell's inequalirty

5.1: Urn problem

5.2: Fisher's maximum likrlihoof method

5.3: Examples of Fisher's maximum likrlihoof method

5.4: Moment method

5.5: Monty Hall problem: High school student puzzle

5.6: Two envelope problem: High school student puzzle

6.1: Review: classical quantum language

6.2: The reverse relation between confidence interval and statistical hypothesis

6.3(1): Population mean (Confidence interval and statistical hypothesis testing)

6.3(2): Population mean (Confidence interval and statistical hypothesis testing)

6.4(1): Population variance (Confidence interval and statistical hypothesis testing)

6.4(2): Population variance (Confidence interval and statistical hypothesis testing)

6.5: Difference of population means (Confidence interval and statistical hypothesis

6.6: Student $t$-distribution of population mean

7.1: Zero way ANOVA (= Student $t$-distribution )

7.2: The one way ANOVA

7.3(1): The two way ANOVA

7.3(2): The two way ANOVA

7.4: Supplement (Gauss integral )

8.1: Marginal observable and quasi-product observable

8.2: Properties of quasi-product observables

8.3: The definition of "implication "

8.4: Cogito-- I think, therefore I am

8.5: Combined observable -- Only one measurement is permitted

8.6: Syllogism-- Does Socrates die?

8.7: Syllogism does not hold in quantum systems

9.1: Mixed measurement theory ( Bayesian statistics )

9.2: Simple examples in mixed measurements

9.3: St. Petersburg two envelope problem

9.4: Bayesian statistics is to use Bayes theorem

9.5: Two envelope problem (Bayes' method)

9.6:Monty Hall problem ( Bayesian approach )

9.7:Monty Hall problem ( The principle of equal weight )

9.8: Averaging information ( Entropy )

9.9: Fisher statistics: Monty Hall problem [three prisoners problem]

9.10:Bayesian statistics: Monty Hall problem [three prisoners problem]

9.11: Equal probability}: Monty Hall problem [three prisoners problem]

9.12: Bertrand's paradox( "randomness" depends on how you look at)

10.1: The most important unsolved problem---what is causality?

10.2: Causality---Mathematical preparation

10.2.2: Simple example---Finite causal operator is represented bymatrix

10.3:Axiom 2---Smoke is not located on the place which does not have fire

10.4: Kinetic equation (in classical mechanics and quantum mechanics)

10.5: Exercise:Solve Schrödinger equation by variable separation method

10.6:Random walk and quantum decoherence

10.7: Leibniz=Clarke Correspondence: What is space-time?

11.1: The Heisenberg picture and the Schrödinger picture

11.2: Wave function collapse ( = Projection postulate )

11.3:de Broglie's paradox(non-locality=faster-than-light)

11.4: Quantum Zeno effect

11.5: Schrödinger's cat, Wigner's friend and Laplace's demon

11.6: Wheeler's Delayed choice experiment: "Particle or wave?" is a foolish question

12.1: Finite realized causal observable

12.2 Double-slit experiment

12.3: Wilson cloud chamber in double slit experiment

12.4: Two kinds of absurdness ---idealism and dualism

13.1: "Inference = Control" in quantum language

13.2: Regression analysis

14.1: Infinite realized causal observable in classical systems

14.2: Is Brownian motion a motion?

14.3: The Schrödinger picture of the sequential deterministic causal operator

14.4 : Zeno's paradoxes---Flying arrow is not moving

15.1 The least squares method

15.2: Regression analysis in quantum language

15.3: Regression analysis(distribution , confidence interval and statistical hypothesis testing)

15.4: Generalized linear model

16.1: Bayes=Kalman method (in $L^\infty(\Omega, m)$)

16.2: Problem establishment (concrete calculation)

16.3: Bayes=Kalman operator

16.4: Calculation: prediction part

16.5: Calculation: Smoothing part

17.1: Equilibrium statistical mechanics (Causality)

17.2: Equilibrium statistical mechanics (Probability)

18.1: Reliability in psychological tests

18.1.3: Reliability coefficient

18.2: Correlation coefficient: How to calculate the reliability coefficient

19.1: Belief, probability and odds

19.2: The principle of equal odds weight

20.2: The summary of quantum language

20.3: Quantum language is located at the center of science