Equal sign

Since aj always is positive or zero, and Ei — Eq always is positive or zero ( o is by definition the lowest energy), this completes the proof. Furthermore, in order for the equal sign to hold, all =0 since , o - q is non-zero (neglecting degenerate ground states). This in turns means that ao = ], owing to the nonnalization of, and consequently the wave function is the exact solution. 

Careful inspection of the result [recall the first term of (3.11)] reveals The equal sign in (3.12) holds for < 12, and strict inequality for n > 13. 

Many chemists use an equals" sign in place of the arrow. Thus, equation (2) would be written ... 

The reversible process (for which the equal sign applies) gives the maximum efficiency for the conversion of heat into work, but even the reversible engine is limited in the extent to which heat can be converted into work. 

Multiply the extremes and place die product (result) to die left of die equal sign. 

Multiply the means and place die product to die right of the equal sign. 

Solve for X by dividing the number to the right of die equal sign by die number to the left of the equal sign (150 -s- 5). 

Then multiply the means and place die product to die left of the equal sign. Then multiply die extremes and place the product to the right of the equal sign. 

If die numbers are die same on both sides of the equal sign, die equation has been solved correctly. 

Step 2. Write die identified unit of measure to be calculated, followed by an equal sign. In the problem above, mL is die unit to be calculated, so the nurse writes ... 

Step 3. Next, the dosage strength is written, witii die numerator always expressed in the same unit that was identified before the equal sign. For example ... 

Step 2. Next, express the dosage strength as a fraction witii die numerator having the same unit of measure as die number before the equal sign. 

A useful convention employs an equal sign for a net reaction, reserving directional arrows for elementary reactions. This practice is not too widely followed, however. 

Most of the examples of chemical equations presented in Table 4.1 include an arrow ( ) symbol. This implies a direction to the chemical change represented this is a process of reactant(s) becoming produces). However, sometimes students meet reactions where an equality sign (=) or a double-headed arrow symbol is... 

Replacing the proportionahty constant with an equal sign by introducing a proportionahty or rate constant k characteristic of the reaction under study gives equations (20) and (21), in which the subscripts 1 and —1 refer to the rate constants for the forward and reverse reactions, respectively. 

The equality sign in (A.4) only holds if the series converges. Otherwise the series is at least asymptotic in the sense that the sum truncated at some k differs from... 

Because the elements of v, all have equal sign, contrary to the elements of V2 which have mixed signs, x, /X2 values satisfying eq. (34.8) are found on the interval [/n,n], where m is equal to... 

Weisskopf and Wigner [2] have shown that the natural width of the emission and the absorption line is readily determined by the mean lifetime x of the excited state because of the relation (note the equal sign) ... 

Note on notation Relations from breakup, coalescence, fragmentation, and aggregation are based on either actual experiments or numerical simulations, the latter commonly referred to as computer experiments. Computer experiments are often based on crude simplifying assumptions and actual experiments are always subject to errors the strict use of the equality sign in many of the final results may therefore be misleading. In order to accurately represent the uncertainty associated with the results, the following notation is adopted ... 

For a mixture of two gases—gas 1 and gas 2—put in equal signs or plus signs in the appropriate places in the equations below ... 

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