Question

It is a curious historical fact that modern quantum mechanics began with two quite different mathematical formulations: the differential equation of Schrödinger, and the matrix algebra of Heisenberg. The two, apparently dissimilar, approaches were proved to be mathematically equivalent. Which of the following sentences would most meaningfully follow the above paragraph?

• A. The two approaches did not start with the same mathematical formulations.
• B. These two points of view were destined to complement one another and were ultimately synthesized in Dirac’s transformation theory.
• C. A third mathematical formulation given by Feynman combines the matrix algebra of Heisenberg and Integral calculus of Leibniz.
• D. Quantum mechanics evolved in the twentieth century and came very close to particle physics, especially after the CERN experiments in Switzerland.
• E. Earlier, the two formulations were mathematically similar.

Hint:

In para-completion questions, always look for the sentence that {extends} the idea instead of repeating or contradicting it. The right answer often provides synthesis or logical consequence.

Answer 1

The Correct Option is B

Step 1: Analyze the context.
The paragraph sets up a contrast: two seemingly dissimilar approaches in quantum mechanics (Schrödinger’s wave mechanics and Heisenberg’s matrix mechanics) were later proven equivalent. The next logical step should describe how they fit together in the evolution of quantum mechanics. Step 2: Evaluate the options.
- (A) Restates what has already been said (redundant).
- (B) Adds a meaningful continuation: explains how the two approaches complemented each other and were synthesized in Dirac’s transformation theory. This flows logically.
- (C) Talks about Feynman, which is historically later, not an immediate continuation.
- (D) Shifts the focus to CERN and particle physics, irrelevant to the immediate discussion.
- (E) Contradicts the given information (they were not “similar” earlier). Step 3: Conclusion.
Thus, option (B) is the most logically coherent continuation. \[ \boxed{\text{These two approaches complemented each other and were unified by Dirac.}} \]