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.

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CONTENTS :PDF + HTML
0.0 Home page
0.1: Preface
1.0: 1.0:Feynman's question
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?)
2.0: Axiom 1( measurement ); Abstract
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
3.0: Linguistic interpretation; Abstract
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
4.0: Linguistic interpretation; quantum systems
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
5.0: Fisher statistics (abstract)
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
6.0: Confidence interval and statistical hypothesis testing ( Abstract )
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
7.0: ANOVA(Analysis of variance) ( Abstract )
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 )
8.0: Practical logic - Do you believe in syllogism?
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
9.0: Mixed measurement theory ($\supset$Bayesian statistics)
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)
10.0: Causality (Abstract)
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?
11.0: Measurement and causality (Abstract)
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
12.0: Realized causal observable in general theory
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
13.0: Fisher statistic (II)
13.1: "Inference = Control" in quantum language
13.2: Regression analysis
14.0: 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
15.0: Least-squares method and Regression analysis
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
16.0: Kalman filter
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
17.0: Equilibrium statistical mechanics

17.1: Equilibrium statistical mechanics (Causality)
17.2: Equilibrium statistical mechanics (Probability)
18.0: The reliability in psychological test
18.1: Reliability in psychological tests
18.1.3: Reliability coefficient
18.2: Correlation coefficient: How to calculate the reliability coefficient
19.0: How to describe "brief"
19.1: Belief, probability and odds
19.2: The principle of equal odds weight
20.1: Two kinds of ( realistic and linguistic ) world- views
20.2: The summary of quantum language
20.3: Quantum language is located at the center of science



:INDEX

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CONTENTS (FC2-version )