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 Copenhagen Interpretation of Quantum Mechanics : Quantum language [ver.4]"

KSTS/RR-18/002 (2018, Research Report in Dept, Math. Keio Univ.)

The following web-version is extracted from the above preprint.
Proofs and detailed calculations are omitted.
But many figures are added.
KSTS/RR-18/002 (2018, Research Report in Dept, Math. Keio Univ.)

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